Homological Algebra Workshop /
|
|
|
- Charles Pope
- 8 years ago
- Views:
Transcription
1 Homological Algebra Workshop / Monday: Tuesday: 9:45 10:00 Registration 10:00 11:15 Conchita Martínez (I) 10:00 11:15 Conchita Martínez (II) 11:15 11:45 Coffee Break 11:15 11:45 Coffee Break 11:45-13:00 Antonio Diaz (I) 11:45-13:00 Antonio Diaz (II) 13:00-15:00 Lunch 13:00-15:00 Lunch 15:00 16:00 Antonio Viruel (I) 15:00-16:00 Antonio Viruel (II) 16:05 16:50 Urban Jezernik 16:05-16:50 Joan Tent 16:55-17:40 Mima Stanojkovski Wednesday: Thursday: 10:00 11:15 Conchita Martínez (III) 10:00 11:15 Conchita Martínez (IV) 11:15 11:45 Coffee Break 11:15 11:45 Coffee Break 11:45-13:00 Antonio Diaz (III) 11:45-13:00 Antonio Diaz (IV) 13:00-15:00 Lunch 13:00-15:00 Lunch Friday: 10:00 11:15 Conchita Martínez (V) 11:15 11:45 Coffee Break 11:45-13:00 Antonio Diaz (V) 15:00-16:00 Ramón Flores 16:05-16:45 Oihana Garaialde 1
2 Introduction to homological algebra Conchita Martínez, Universidad de Zaragoza 1. Chain complexes: Homology, maps between chain complexes. Simplicial and CW-complexes. Homotopy equivalences and weak equivalences. 2. Projective, injective and flat resolutions. Free, projective, injective and flat modules. Resolutions. Comparison Lemma. 3. Ext and Tor. Ext using projectives. Examples. Derived funtors. Examples in abelian groups and group (co)homology. 4. Snake Lemma. Long exact sequences. Mapping cone. Ext using injectives. 5. Tools. Mayer-vietoris. Universal coefficients theorem. Shapiro. Limits and colimits. 6. Group cohomology and finiteness properties. Milnor construction. Cayley graphs. Finite presentability, properties F, FP, FP n, cohomological dimension. Examples. 7. Cohomology with bounded support. Coxeter groups. 2
3 Spectral sequences Antonio Díaz, Universidad de Málaga This course is an introduction to spectral sequences. Proofs will be given only for the essential constructions. There will be plenty of examples to get used to spectral sequences and to learn how to compute with them. The intended program is as follows: Day 1: Spectral sequences as a black box. (a) Spectral sequences of differential modules. Convergence. Extension problems. (b) Spectral sequences of algebras. Lifting problems. (c) Exploiting the gaps. Working backwards. Day 2: Inside the black box. (a) The spectral sequence of a filtered differential module. Exact couples. (b) The spectral sequence of a double differential complex. (c) Comparison theorems. Day 3: Spectral sequences in group cohomology. (a) The Lyndon-Hochschild-Serre spectral sequence. (b) Central extensions. Wreath products. LHS stops. (c) Cohomology of finite abelian groups. Day 4: Spectral sequences in algebraic topology. (a) Basics about algebraic topology. (b) Leray-Serre spectral sequence. (c) Applications. Day 5: Other spectral sequences in algebra and topology. 3
4 Bibliography For spectral sequences: J. McCleary, A User s Guide to Spectral Sequences (Cambridge Studies in Advanced Mathematics 58), Cambridge University Press, C.A. Weibel, An Introduction to Homological Algebra (Cambridge Studies in Advanced Mathematics 38), Cambridge University Press, S. MacLane, Homology (Classics in Mathematics), Springer, A. Hatcher, Spectral sequences in algebraic topology, hatcher/ssat/ssatpage.html For group cohomology: K.S. Brown, Cohomology of Groups (Graduate Texts in Mathematics, No. 87), Springer, L. Evens, The Cohomology of Groups (Oxford Mathematical Monographs), OUP Oxford, A. Adem, R.J. Milgram, Cohomology of Finite Groups (Grundlehren der mathematischen Wissenschaften), Springer, For algebraic topology: A. Hatcher, Algebraic Topology, hatcher/at/atpage.html R.M. Switzer, Algebraic topology homotopy and homology (Classics in Mathematics), Springer-Verlag, Further references: R. Bieri, Homological dimension of discrete groups. Queen Mary College Mathematical Notes. Queen Mary College Department of Pure Mathematics, London, second edition, M. Davis. The geometry and topology of Coxeter groups. London Math. Soc. Monographs Series, 32. Princeton Un. Press, Princeton, NJ, R. Geoghegan. Topological Methods in Group Theory. Graduate Texts in Mathematics. Springer-Verlag,
5 A modified version of the Bousfield-Kan tower Ramón Flores In this talk we present a modified version of the Bousfield-Kan tower for topological spaces, and explain its relation with the classical tower. We will describe some relations of these functors with the profinite group completion. Cohomology of p-groups and Carlson s conjecture Oihana Garaialde Ocaña Let G be a p-group of order p n. If c denotes the class of G, then the coclass of G is n c. Leedham-Green and Newman suggested to classify p-groups by coclass. In fact, Leedham-Green has shown that every p-group of fixed coclass "comes from" a finite number of p-adic uniserial space groups. Using the result for p = 2, Jon F. Carlson proved that there are only finitely many algebras for the cohomology H (G; F 2 ) with trivial coefficients in the finite field of 2 elements. In the same paper, he formulates a conjecture stating that the same result should hold for p odd. In this talk, we give a method to show that certain groups have isomorphic cohomology rings and we will give an outline of the steps to answer Carlson s conjecture. The Schur multiplier Urban Jezernik The Schur multiplier is a homological invariant of groups. Basic by nature, yet quite erratic in behaviour. I will present a very much elementary way of looking at this group and illustrate some advantages that such an approach offers. Evolving groups Stanojkovski, Mima Evolving groups arise as a solution to a question that is inspired from phenomena occurring in Galois cohomology. We will formalize the problem and give a characterization. A cohomological criterion for p-solvability Joan Tent Jorques We shall present a criterion for a finite group to be p-solvable based on Tate s p-nilpotency criterion. Related to this, we shall also prove some results relating the number of generators of a Sylow p-subgroup of G with other invariants of the group. This is joint work with Jon González. 5
6 Cohomological uniqueness of groups Antonio Viruel The Isomorphism Problem in a category C consists on providing a procedure that determines whether two objects in C are isomorphic or not. If such a procedure exists and the techniques fit into some theory T, it is said that T tells objects in C apart. In this talk we address the question of whether (finite) groups are told apart if we consider mod p cohomology. We shall present the so far only known general strategy to answer this question, and show how different flavors of mod p cohomology lead to cohomological uniqueness of different families of groups. 6
Kyoto University. Note on the cohomology of finite cyclic coverings. Yasuhiro Hara and Daisuke Kishimoto
Kyoto University Kyoto-Math 2013-02 Note on the cohomology of finite cyclic coverings by Yasuhiro Hara and Daisuke Kishimoto April 2013 Department of Mathematics Faculty of Science Kyoto University Kyoto
BP-cohomology of mapping spaces from the classifying space of a torus to some p-torsion free space
BP-cohomology of mapping spaces from the classifying space of a torus to some p-torsion free space 1. Introduction Let p be a fixed prime number, V a group isomorphic to (Z/p) d for some integer d and
NOTES ON CATEGORIES AND FUNCTORS
NOTES ON CATEGORIES AND FUNCTORS These notes collect basic definitions and facts about categories and functors that have been mentioned in the Homological Algebra course. For further reading about category
Online publication date: 11 March 2010 PLEASE SCROLL DOWN FOR ARTICLE
This article was downloaded by: [Modoi, George Ciprian] On: 12 March 2010 Access details: Access Details: [subscription number 919828804] Publisher Taylor & Francis Informa Ltd Registered in England and
COHOMOLOGY OF GROUPS
Actes, Congrès intern. Math., 1970. Tome 2, p. 47 à 51. COHOMOLOGY OF GROUPS by Daniel QUILLEN * This is a report of research done at the Institute for Advanced Study the past year. It includes some general
Allen Back. Oct. 29, 2009
Allen Back Oct. 29, 2009 Notation:(anachronistic) Let the coefficient ring k be Q in the case of toral ( (S 1 ) n) actions and Z p in the case of Z p tori ( (Z p )). Notation:(anachronistic) Let the coefficient
Lectures on the Cohomology of Finite Groups
Contemporary Mathematics Lectures on the Cohomology of Finite Groups Alejandro Adem Abstract. These are notes based on lectures given at the summer school Interactions Between Homotopy Theory and Algebra,
Groups with the same orders and large character degrees as PGL(2, 9) 1. Introduction and preliminary results
Quasigroups and Related Systems 21 (2013), 239 243 Groups with the same orders and large character degrees as PGL(2, 9) Behrooz Khosravi Abstract. An interesting class of problems in character theory arises
Math 231b Lecture 35. G. Quick
Math 231b Lecture 35 G. Quick 35. Lecture 35: Sphere bundles and the Adams conjecture 35.1. Sphere bundles. Let X be a connected finite cell complex. We saw that the J-homomorphism could be defined by
Effective homotopy of the fiber of a Kan fibration
Effective homotopy of the fiber of a Kan fibration Ana Romero and Francis Sergeraert 1 Introduction Inspired by the fundamental ideas of the effective homology method (see [5] and [4]), which makes it
Galois representations with open image
Galois representations with open image Ralph Greenberg University of Washington Seattle, Washington, USA May 7th, 2011 Introduction This talk will be about representations of the absolute Galois group
Algebraic Morava K-theories and the. higher degree formula
Algebraic Morava K-theories and the higher degree formula 1 Contents Chapter 1. Introduction 1 Chapter 2. The construction of an algebraic Morava K-theory spectrum 5 Chapter 3. The theorem in the general
A NOTE ON TRIVIAL FIBRATIONS
A NOTE ON TRIVIAL FIBRATIONS Petar Pavešić Fakulteta za Matematiko in Fiziko, Univerza v Ljubljani, Jadranska 19, 1111 Ljubljana, Slovenija petar.pavesic@fmf.uni-lj.si Abstract We study the conditions
ON GENERALIZED RELATIVE COMMUTATIVITY DEGREE OF A FINITE GROUP. A. K. Das and R. K. Nath
International Electronic Journal of Algebra Volume 7 (2010) 140-151 ON GENERALIZED RELATIVE COMMUTATIVITY DEGREE OF A FINITE GROUP A. K. Das and R. K. Nath Received: 12 October 2009; Revised: 15 December
On the existence of G-equivariant maps
CADERNOS DE MATEMÁTICA 12, 69 76 May (2011) ARTIGO NÚMERO SMA# 345 On the existence of G-equivariant maps Denise de Mattos * Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação,
COMPUTING WITH HOMOTOPY 1- AND 2-TYPES WHY? HOW? Graham Ellis NUI Galway, Ireland
COMPUTING WITH HOMOTOPY 1- AND 2-TYPES WHY? HOW? Graham Ellis NUI Galway, Ireland Why: 1. potential applications to data analysis 2. examples for generating theory How: 3. discrete Morse theory 4. homological
Fixed Point Theory. With 14 Illustrations. %1 Springer
Andrzej Granas James Dugundji Fixed Point Theory With 14 Illustrations %1 Springer Contents Preface vii 0. Introduction 1 1. Fixed Point Spaces 1 2. Forming New Fixed Point Spaces from Old 3 3. Topological
How To Prove The Cellosauric Cardinal Compactness (For A Cardinal Cardinal Compact)
Cellular objects and Shelah s singular compactness theorem Logic Colloquium 2015 Helsinki Tibor Beke 1 Jiří Rosický 2 1 University of Massachusetts tibor beke@uml.edu 2 Masaryk University Brno rosicky@math.muni.cz
MA651 Topology. Lecture 6. Separation Axioms.
MA651 Topology. Lecture 6. Separation Axioms. This text is based on the following books: Fundamental concepts of topology by Peter O Neil Elements of Mathematics: General Topology by Nicolas Bourbaki Counterexamples
Sign changes of Hecke eigenvalues of Siegel cusp forms of degree 2
Sign changes of Hecke eigenvalues of Siegel cusp forms of degree 2 Ameya Pitale, Ralf Schmidt 2 Abstract Let µ(n), n > 0, be the sequence of Hecke eigenvalues of a cuspidal Siegel eigenform F of degree
A CONSTRUCTION OF THE UNIVERSAL COVER AS A FIBER BUNDLE
A CONSTRUCTION OF THE UNIVERSAL COVER AS A FIBER BUNDLE DANIEL A. RAMRAS In these notes we present a construction of the universal cover of a path connected, locally path connected, and semi-locally simply
(Part 2) Lunch Block 7 1:05 PM 2:27 PM
Wednesday, December 2 (5,1,3,7) Cycle day 3 Module 1 of the Algebra I Exam 4 BLOCK DAY LUNCHES ASSIGNED BY LOCATION DURING 3 RD. 2 nd floor classes (unless assigned b lunch below): A lunch Basement, Health,
Sets of Fibre Homotopy Classes and Twisted Order Parameter Spaces
Communications in Mathematical Physics Manuscript-Nr. (will be inserted by hand later) Sets of Fibre Homotopy Classes and Twisted Order Parameter Spaces Stefan Bechtluft-Sachs, Marco Hien Naturwissenschaftliche
AXIOMS FOR INVARIANT FACTORS*
PORTUGALIAE MATHEMATICA Vol 54 Fasc 3 1997 AXIOMS FOR INVARIANT FACTORS* João Filipe Queiró Abstract: We show that the invariant factors of matrices over certain types of rings are characterized by a short
Analytic cohomology groups in top degrees of Zariski open sets in P n
Analytic cohomology groups in top degrees of Zariski open sets in P n Gabriel Chiriacescu, Mihnea Colţoiu, Cezar Joiţa Dedicated to Professor Cabiria Andreian Cazacu on her 80 th birthday 1 Introduction
Every tree contains a large induced subgraph with all degrees odd
Every tree contains a large induced subgraph with all degrees odd A.J. Radcliffe Carnegie Mellon University, Pittsburgh, PA A.D. Scott Department of Pure Mathematics and Mathematical Statistics University
Ideal Class Group and Units
Chapter 4 Ideal Class Group and Units We are now interested in understanding two aspects of ring of integers of number fields: how principal they are (that is, what is the proportion of principal ideals
FIBRATION SEQUENCES AND PULLBACK SQUARES. Contents. 2. Connectivity and fiber sequences. 3
FIRTION SEQUENES ND PULLK SQURES RY MLKIEWIH bstract. We lay out some foundational facts about fibration sequences and pullback squares of topological spaces. We pay careful attention to connectivity ranges
Row Ideals and Fibers of Morphisms
Michigan Math. J. 57 (2008) Row Ideals and Fibers of Morphisms David Eisenbud & Bernd Ulrich Affectionately dedicated to Mel Hochster, who has been an inspiration to us for many years, on the occasion
CONSEQUENCES OF THE SYLOW THEOREMS
CONSEQUENCES OF THE SYLOW THEOREMS KEITH CONRAD For a group theorist, Sylow s Theorem is such a basic tool, and so fundamental, that it is used almost without thinking, like breathing. Geoff Robinson 1.
F. ABTAHI and M. ZARRIN. (Communicated by J. Goldstein)
Journal of Algerian Mathematical Society Vol. 1, pp. 1 6 1 CONCERNING THE l p -CONJECTURE FOR DISCRETE SEMIGROUPS F. ABTAHI and M. ZARRIN (Communicated by J. Goldstein) Abstract. For 2 < p
A List of Recommended Books in Topology
A List of Recommended Books in Topology Allen Hatcher These are books that I personally like for one reason or another, or at least find useful. They range from elementary to advanced, but don t cover
Smith Theory Revisited
Smith Theory Revisited William G. Dwyer Clarence W. Wilkerson 1 Introduction In the late 1930 s, P. A. Smith began the investigation of the cohomological properties of a group G of prime order p acting
How To Find Out How To Build An Elliptic Curve Over A Number Field
Numbers Volume 2015, Article ID 501629, 4 pages http://dx.doi.org/10.1155/2015/501629 Research Article On the Rank of Elliptic Curves in Elementary Cubic Extensions Rintaro Kozuma College of International
Curriculum Vitae Tomas Everaert
Curriculum Vitae Tomas Everaert 1 General Information 1. Surname, First Name: Everaert, Tomas 2. Place and Date of Birth: Belgium, Ostend, June 3, 1980 3. Nationality: Belgian 4. Legal Address: Korte Hofstraat
EXERCISES FOR THE COURSE MATH 570, FALL 2010
EXERCISES FOR THE COURSE MATH 570, FALL 2010 EYAL Z. GOREN (1) Let G be a group and H Z(G) a subgroup such that G/H is cyclic. Prove that G is abelian. Conclude that every group of order p 2 (p a prime
Mathematics Course 111: Algebra I Part IV: Vector Spaces
Mathematics Course 111: Algebra I Part IV: Vector Spaces D. R. Wilkins Academic Year 1996-7 9 Vector Spaces A vector space over some field K is an algebraic structure consisting of a set V on which are
A REMARK ON ALMOST MOORE DIGRAPHS OF DEGREE THREE. 1. Introduction and Preliminaries
Acta Math. Univ. Comenianae Vol. LXVI, 2(1997), pp. 285 291 285 A REMARK ON ALMOST MOORE DIGRAPHS OF DEGREE THREE E. T. BASKORO, M. MILLER and J. ŠIRÁŇ Abstract. It is well known that Moore digraphs do
On the Multiplier of a Lie Algebra
Journal of Lie Theory Volume 13 (003) 1 6 c 003 Heldermann Verlag On the Multiplier of a Lie Algebra Bill Yankosky Communicated by J. D. Lawson Abstract. Under fairly general conditions, we extend the
FINAL SCHEDULE YEAR 1 AUGUST 18 22 WEEK 1
YEAR 1 AUGUST 18 22 WEEK 1 TIME MONDAY (18) TUESDAY (19) WEDNESDAY (20) THURSDAY (21) FRIDAY (22) 11am 1 LUNCH LUNCH LUNCH LUNCH LUNCH 3 YEAR 1 AUGUST 25 29 WEEK 2 TIME MONDAY (25) TUESDAY (26) WEDNESDAY
FACTORING POLYNOMIALS IN THE RING OF FORMAL POWER SERIES OVER Z
FACTORING POLYNOMIALS IN THE RING OF FORMAL POWER SERIES OVER Z DANIEL BIRMAJER, JUAN B GIL, AND MICHAEL WEINER Abstract We consider polynomials with integer coefficients and discuss their factorization
CURRICULUM VITAE. 2006-2013 President of the Board of Directors of the Annales des Sciences Mathématiques du Québec.
CURRICULUM VITAE François Huard Department of Mathematics Bishop s University, Sherbrooke, Québec Canada, J1M1Z7 819-822-9600 (2363) email:fhuard@ubishops.ca Languages: French, English. Citizenship: Canadian
You Could Have Invented Spectral Sequences
You Could Have Invented Spectral Sequences Timothy Y Chow Introduction The subject of spectral sequences has a reputation for being difficult for the beginner Even G W Whitehead (quoted in John McCleary
Fiber bundles and non-abelian cohomology
Fiber bundles and non-abelian cohomology Nicolas Addington April 22, 2007 Abstract The transition maps of a fiber bundle are often said to satisfy the cocycle condition. If we take this terminology seriously
arxiv:1209.1368v1 [math.sg] 6 Sep 2012
![arxiv:1209.1368v1 [math.sg] 6 Sep 2012](/thumbs/25/4769068.jpg "arxiv:1209.1368v1 [math.sg] 6 Sep 2012")
ISOTOPY CLASSIFICATION OF ENGEL STRUCTURES ON CIRCLE BUNDLES MIRKO KLUKAS AND BIJAN SAHAMIE arxiv:1209.1368v1 [math.sg] 6 Sep 2012 Abstract. We call two Engel structures isotopic if they are homotopic
Characterization Of Polynomials Using Reflection Coefficients
Applied Mathematics E-Notes, 4(2004), 114-121 c ISSN 1607-2510 Available free at mirror sites of http://www.math.nthu.edu.tw/ amen/ Characterization Of Polynomials Using Reflection Coefficients José LuisDíaz-Barrero,JuanJosé
Groups of Prime Power Order
de Gruyter Expositions in Mathematics 56 Groups of Prime Power Order Volume 3 Bearbeitet von Yakov Berkovich, Zvonimir Janko 1. Auflage 2011. Buch. XXV, 639 S. Hardcover ISBN 978 3 11 020717 0 Format (B
TRANSFERS OF CHERN CLASSES IN BP-COHOMOLOGY AND CHOW RINGS. 1. Introduction
TRANSFERS OF CHERN CLASSES IN BP-COHOMOLOGY AND CHOW RINGS Abstract. The BP -module structures of BP (BG) for extraspecial 2-groups are studied using transfer and Chern classes. These give rise to p-torsion
How To Prove The Dirichlet Unit Theorem
Chapter 6 The Dirichlet Unit Theorem As usual, we will be working in the ring B of algebraic integers of a number field L. Two factorizations of an element of B are regarded as essentially the same if
RESEARCH STATEMENT AMANDA KNECHT
RESEARCH STATEMENT AMANDA KNECHT 1. Introduction A variety X over a field K is the vanishing set of a finite number of polynomials whose coefficients are elements of K: X := {(x 1,..., x n ) K n : f i
A DETERMINATION OF ALL NORMAL DIVISION ALGEBRAS OVER AN ALGEBRAIC NUMBER FIELD*
A DETERMINATION OF ALL NORMAL DIVISION ALGEBRAS OVER AN ALGEBRAIC NUMBER FIELD* BY A. ADRIAN ALBERT AND HELMUT HASSE t 1. Introduction. The principal problem in the theory of linear algebras is that of
IRREDUCIBLE OPERATOR SEMIGROUPS SUCH THAT AB AND BA ARE PROPORTIONAL. 1. Introduction
IRREDUCIBLE OPERATOR SEMIGROUPS SUCH THAT AB AND BA ARE PROPORTIONAL R. DRNOVŠEK, T. KOŠIR Dedicated to Prof. Heydar Radjavi on the occasion of his seventieth birthday. Abstract. Let S be an irreducible
Duality of linear conic problems
Duality of linear conic problems Alexander Shapiro and Arkadi Nemirovski Abstract It is well known that the optimal values of a linear programming problem and its dual are equal to each other if at least
ON COMPLETELY CONTINUOUS INTEGRATION OPERATORS OF A VECTOR MEASURE. 1. Introduction
ON COMPLETELY CONTINUOUS INTEGRATION OPERATORS OF A VECTOR MEASURE J.M. CALABUIG, J. RODRÍGUEZ, AND E.A. SÁNCHEZ-PÉREZ Abstract. Let m be a vector measure taking values in a Banach space X. We prove that
Topological Algebraic Geometry Workshop Oslo, September 4th-8th, 2006. Spectra associated with Artin-Schreier curves. Doug Ravenel
Topological Algebraic Geometry Workshop Oslo, September 4th-8th, 2006 Spectra associated with Artin-Schreier curves Doug Ravenel University of Rochester September 6, 2006 1 2 1. My favorite part of the
Cycles in a Graph Whose Lengths Differ by One or Two
Cycles in a Graph Whose Lengths Differ by One or Two J. A. Bondy 1 and A. Vince 2 1 LABORATOIRE DE MATHÉMATIQUES DISCRÉTES UNIVERSITÉ CLAUDE-BERNARD LYON 1 69622 VILLEURBANNE, FRANCE 2 DEPARTMENT OF MATHEMATICS
Q-PERFECT GROUPS AND UNIVERSAL Q-CENTRAL EXTENSIONS
Publicacions Matemátiques, Vol 34 (1990), 291-297. Q-PERFECT GROUPS AND UNIVERSAL Q-CENTRAL EXTENSIONS RONALD BROWN Abstract Using results of Ellis-Rodríguez Fernández, an explicit description by generators
Punch Maps in Numerology
Math. Proc. Camb. Phil. Soc. (1986), 99, 59 59 Printed in Qreat Britain Note on desuspending the Adams map BY F. R. COHEN AND J. A. NEISENDORFER University of Kentucky and Ohio State University (Received
Academic Calendar for Faculty
Summer 2013 Term June 3, 2013 (Monday) June 3-4, 2013 (Monday Tuesday) June 5, 2013 (Wednesday) June 5-6, 2013 (Wednesday Thursday) June 6, 2013 (Thursday) July 3, 2013 (Wednesday) July 4, 2013 (Thursday)
THE HOPF RING FOR COMPLEX COBORDISM 1 BY DOUGLAS C. RAVENEL AND W. STEPHEN WILSON. Communicated by Edgar Brown, Jr., May 13, 1974
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY Volume 80, Number 6, November 1974 THE HOPF RING FOR COMPLEX COBORDISM 1 BY DOUGLAS C. RAVENEL AND W. STEPHEN WILSON Communicated by Edgar Brown, Jr., May
FIXED POINT SETS OF FIBER-PRESERVING MAPS
FIXED POINT SETS OF FIBER-PRESERVING MAPS Robert F. Brown Department of Mathematics University of California Los Angeles, CA 90095 e-mail: rfb@math.ucla.edu Christina L. Soderlund Department of Mathematics
Chapter 7. Permutation Groups
Chapter 7 Permutation Groups () We started the study of groups by considering planar isometries In the previous chapter, we learnt that finite groups of planar isometries can only be cyclic or dihedral
LMC Tutoring Program Math Tutor Application
LMC Tutoring Program Math Tutor Application Dear LMC Student: Thank you for your interest in working for the LMC Math Tutoring Program. In order to become a tutor, you must meet the following qualifications
OSTROWSKI FOR NUMBER FIELDS
OSTROWSKI FOR NUMBER FIELDS KEITH CONRAD Ostrowski classified the nontrivial absolute values on Q: up to equivalence, they are the usual (archimedean) absolute value and the p-adic absolute values for
Computational homology of n-types
Computational homology of n-types Graham Ellis Graham Ellis, School of Mathematics, National University of Ireland, Galway Le Van Luyen Le Van Luyen, School of Mathematics, National University of Ireland,
Prime Numbers and Irreducible Polynomials
Prime Numbers and Irreducible Polynomials M. Ram Murty The similarity between prime numbers and irreducible polynomials has been a dominant theme in the development of number theory and algebraic geometry.
Allocation of Mathematics Modules at Maynooth to Areas of Study for PME (Professional Masters in Education)
Allocation of Mathematics Modules at Maynooth to Areas of Study for PME (Professional Masters in Education) Module Code Module Title Credits Area 1 Area 2 MT101 Differential Calculus In One Real Variable
THE FUNDAMENTAL THEOREM OF ALGEBRA VIA PROPER MAPS
THE FUNDAMENTAL THEOREM OF ALGEBRA VIA PROPER MAPS KEITH CONRAD 1. Introduction The Fundamental Theorem of Algebra says every nonconstant polynomial with complex coefficients can be factored into linear
Universitat de Barcelona
Universitat de Barcelona GRAU DE MATEMÀTIQUES Final year project Cohomology of Product Spaces from a Categorical Viewpoint Álvaro Torras supervised by Prof. Carles Casacuberta January 18, 2016 2 3 Introduction
MATHEMATICS 152, FALL 2004 METHODS OF DISCRETE MATHEMATICS
MATHEMATICS 152, FALL 2004 METHODS OF DISCRETE MATHEMATICS Last revised: September 14, 2004 Instructor: Paul Bamberg Offices: SC 423, 495-1748 and Quincy House 102, 493-3100. Quincy 102 opens off the Quincy
Continued Fractions and the Euclidean Algorithm
Continued Fractions and the Euclidean Algorithm Lecture notes prepared for MATH 326, Spring 997 Department of Mathematics and Statistics University at Albany William F Hammond Table of Contents Introduction
RIGIDITY OF HOLOMORPHIC MAPS BETWEEN FIBER SPACES
RIGIDITY OF HOLOMORPHIC MAPS BETWEEN FIBER SPACES GAUTAM BHARALI AND INDRANIL BISWAS Abstract. In the study of holomorphic maps, the term rigidity refers to certain types of results that give us very specific
Spherical Classes Detected by the Algebraic Transfer
Vietnam Journal of Mathematics 25:l (1997 75 79 Vil.etnann./ourrnatrof l$4atlt{lem.i\]f ltcs 6 Springer-Verlag 1997 Short Communication Spherical Classes Detected by the Algebraic Transfer Nguyen Huu Viet
8.1 Examples, definitions, and basic properties
8 De Rham cohomology Last updated: May 21, 211. 8.1 Examples, definitions, and basic properties A k-form ω Ω k (M) is closed if dω =. It is exact if there is a (k 1)-form σ Ω k 1 (M) such that dσ = ω.
Classical theorems on hyperbolic triangles from a projective point of view
tmcs-szilasi 2012/3/1 0:14 page 175 #1 10/1 (2012), 175 181 Classical theorems on hyperbolic triangles from a projective point of view Zoltán Szilasi Abstract. Using the Cayley-Klein model of hyperbolic
On The Existence Of Flips
On The Existence Of Flips Hacon and McKernan s paper, arxiv alg-geom/0507597 Brian Lehmann, February 2007 1 Introduction References: Hacon and McKernan s paper, as above. Kollár and Mori, Birational Geometry
Miodrag Cristian Iovanov
Miodrag Cristian Iovanov Address: 3333 W 2nd St. #55-215 Los Angeles, CA 90004, USA email: iovanov@usc.edu, yovanov@gmail.com; miovanov@buffalo.edu web: http://yovanov.net Current position Assistant Professor
FIBER PRODUCTS AND ZARISKI SHEAVES
FIBER PRODUCTS AND ZARISKI SHEAVES BRIAN OSSERMAN 1. Fiber products and Zariski sheaves We recall the definition of a fiber product: Definition 1.1. Let C be a category, and X, Y, Z objects of C. Fix also
THE AVERAGE DEGREE OF AN IRREDUCIBLE CHARACTER OF A FINITE GROUP
THE AVERAGE DEGREE OF AN IRREDUCIBLE CHARACTER OF A FINITE GROUP by I. M. Isaacs Mathematics Department University of Wisconsin 480 Lincoln Dr. Madison, WI 53706 USA E-Mail: isaacs@math.wisc.edu Maria
COFINAL MAXIMAL CHAINS IN THE TURING DEGREES
COFINA MAXIMA CHAINS IN THE TURING DEGREES WEI WANG, IUZHEN WU, AND IANG YU Abstract. Assuming ZF C, we prove that CH holds if and only if there exists a cofinal maximal chain of order type ω 1 in the
CONTINUED FRACTIONS AND FACTORING. Niels Lauritzen
CONTINUED FRACTIONS AND FACTORING Niels Lauritzen ii NIELS LAURITZEN DEPARTMENT OF MATHEMATICAL SCIENCES UNIVERSITY OF AARHUS, DENMARK EMAIL: niels@imf.au.dk URL: http://home.imf.au.dk/niels/ Contents
CONTRIBUTIONS TO ZERO SUM PROBLEMS
CONTRIBUTIONS TO ZERO SUM PROBLEMS S. D. ADHIKARI, Y. G. CHEN, J. B. FRIEDLANDER, S. V. KONYAGIN AND F. PAPPALARDI Abstract. A prototype of zero sum theorems, the well known theorem of Erdős, Ginzburg
Fiber sums of genus 2 Lefschetz fibrations
Proceedings of 9 th Gökova Geometry-Topology Conference, pp, 1 10 Fiber sums of genus 2 Lefschetz fibrations Denis Auroux Abstract. Using the recent results of Siebert and Tian about the holomorphicity
Pro-p Groups with Few Normal Subgroups
p. 1/1 Pro-p Groups with Few Normal Subgroups Y. Barnea, N. Gavioli, A. Jaikin-Zapirain, V. Monti, C. M. Scoppola p. 2/1 1. On p-groups of Finite Coclass In this talk p stands for a prime number. For simplicity
A NEW CONSTRUCTION OF 6-MANIFOLDS
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 360, Number 8, August 2008, Pages 4409 4424 S 0002-9947(08)04462-0 Article electronically published on March 12, 2008 A NEW CONSTRUCTION OF 6-MANIFOLDS
DEGREES OF ORDERS ON TORSION-FREE ABELIAN GROUPS
DEGREES OF ORDERS ON TORSION-FREE ABELIAN GROUPS ASHER M. KACH, KAREN LANGE, AND REED SOLOMON Abstract. We construct two computable presentations of computable torsion-free abelian groups, one of isomorphism
SMOOTH CASE FOR T or Z
SMOOTH CASE FOR T or Z Preliminaries. Theorem [DDK] Let F be a simply finite connected CW-complex and E 0 (F ) be the connected component of identity of the space of all homotopy equivalences F F. Then
Symplectic structures on fiber bundles
Symplectic structures on fiber bundles François Lalonde Université du Québec à Montréal (flalonde@math.uqam.ca) Dusa McDuff State University of New York at Stony Brook (dusa@math.sunysb.edu) Aug 27, 2000,
FACTORING CERTAIN INFINITE ABELIAN GROUPS BY DISTORTED CYCLIC SUBSETS
International Electronic Journal of Algebra Volume 6 (2009) 95-106 FACTORING CERTAIN INFINITE ABELIAN GROUPS BY DISTORTED CYCLIC SUBSETS Sándor Szabó Received: 11 November 2008; Revised: 13 March 2009
The Open University s repository of research publications and other research outputs
Open Research Online The Open University s repository of research publications and other research outputs The degree-diameter problem for circulant graphs of degree 8 and 9 Journal Article How to cite:
FINITE NONSOLVABLE GROUPS WITH MANY DISTINCT CHARACTER DEGREES
FINITE NONSOLVABLE GROUPS WITH MANY DISTINCT CHARACTER DEGREES HUNG P. TONG-VIET Abstract. Let G be a finite group and let Irr(G) denote the set of all complex irreducible characters of G. Let cd(g) be
CONTINUED FRACTIONS AND PELL S EQUATION. Contents 1. Continued Fractions 1 2. Solution to Pell s Equation 9 References 12
CONTINUED FRACTIONS AND PELL S EQUATION SEUNG HYUN YANG Abstract. In this REU paper, I will use some important characteristics of continued fractions to give the complete set of solutions to Pell s equation.
An Overview of the Degree/Diameter Problem for Directed, Undirected and Mixed Graphs
Mirka Miller (invited speaker) University of Newcastle, Australia University of West Bohemia, Pilsen King s College, London Abstract A well-known fundamental problem in extremal graph theory is the degree/diameter
PARTITION COMPLEXES, TITS BUILDINGS AND SYMMETRIC PRODUCTS
PARTITION COMPLEXES, TITS BUILDINGS AND SYMMETRIC PRODUCTS G. Z. ARONE AND W. G. DWYER Abstract. We construct a homological approximation to the partition complex, and identify it as the Tits building.
The number of generalized balanced lines
The number of generalized balanced lines David Orden Pedro Ramos Gelasio Salazar Abstract Let S be a set of r red points and b = r + 2δ blue points in general position in the plane, with δ 0. A line l
An inequality for the group chromatic number of a graph
An inequality for the group chromatic number of a graph Hong-Jian Lai 1, Xiangwen Li 2 and Gexin Yu 3 1 Department of Mathematics, West Virginia University Morgantown, WV 26505 USA 2 Department of Mathematics
POLYNOMIAL RINGS AND UNIQUE FACTORIZATION DOMAINS
POLYNOMIAL RINGS AND UNIQUE FACTORIZATION DOMAINS RUSS WOODROOFE 1. Unique Factorization Domains Throughout the following, we think of R as sitting inside R[x] as the constant polynomials (of degree 0).
ANALYTICITY OF SETS ASSOCIATED TO LELONG NUMBERS AND THE EXTENSION OF MEROMORPHIC MAPS 1
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY Volume 79, Number 6, November 1973 ANALYTICITY OF SETS ASSOCIATED TO LELONG NUMBERS AND THE EXTENSION OF MEROMORPHIC MAPS 1 BY YUM-TONG SIU 2 Communicated
WHEN DOES A CROSS PRODUCT ON R n EXIST?
WHEN DOES A CROSS PRODUCT ON R n EXIST? PETER F. MCLOUGHLIN It is probably safe to say that just about everyone reading this article is familiar with the cross product and the dot product. However, what
Alex, I will take congruent numbers for one million dollars please
Alex, I will take congruent numbers for one million dollars please Jim L. Brown The Ohio State University Columbus, OH 4310 jimlb@math.ohio-state.edu One of the most alluring aspectives of number theory