Vector fields on Singular Varieties
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1 Lecture Notes in Mathematics 1987 Vector fields on Singular Varieties Bearbeitet von Jean-Paul Brasselet, José Seade, Tatsuo Suwa 1. Auflage Taschenbuch. xx, 232 S. Paperback ISBN Format (B x L): 15,5 x 23,5 cm Gewicht: 800 g Weitere Fachgebiete > Mathematik > Mathematische Analysis Zu Leseprobe schnell und portofrei erhältlich bei Die Online-Fachbuchhandlung beck-shop.de ist spezialisiert auf Fachbücher, insbesondere Recht, Steuern und Wirtschaft. Im Sortiment finden Sie alle Medien (Bücher, Zeitschriften, CDs, ebooks, etc.) aller Verlage. Ergänzt wird das Programm durch Services wie Neuerscheinungsdienst oder Zusammenstellungen von Büchern zu Sonderpreisen. Der Shop führt mehr als 8 Millionen Produkte.
2 Contents 1 The Case of Manifolds Poincaré Hopf Index Theorem Poincaré Hopf Index at Isolated Points Poincaré Hopf Index at Nonisolated Points Poincaré and Alexander Dualities Chern Classes via Obstruction Theory Chern Classes of Almost Complex Manifolds Relative Chern Classes Chern Weil Theory of Characteristic Classes Čech-de Rham Cohomology Integration on the Čech-de Rham Cohomology Relative Čech-de Rham Cohomology Alexander Duality Localization of Chern Classes Characteristic Classes in the Čech-de Rham Cohomology Localization of Characteristic Classes of Complex Vector Bundles Localization of the Top Chern Class Hyperplane Bundle Grothendieck Residues Residues at an Isolated Zero Examples The Schwartz Index Isolated Singularity Case Whitney Stratifications Radial Extension of Vector Fields The Schwartz Index on a Stratified Variety Case of Vector Fields with an Isolated Singularity Case of Vector Fields with Nonisolated Singularity.. 38 ix
3 x Contents 3 The GSV Index Vector Fields Tangent to a Hypersurface The Index for Vector Fields on ICIS Some Applications and Examples The Case of Isolated Smoothable Singularities Nonisolated Singularities The Strict Thom Condition for Complex Analytic Maps The Hypersurface Case The Complete Intersection Case The Proportionality Theorem Geometric Applications Topological Invariance of the Milnor Number The Canonical Contact Structure on the Link On the Normal Bundle of Holomorphic Singular Foliations Indices of Vector Fields on Real Analytic Varieties The Schwartz Index on Real Analytic Varieties The GSV Index on Real Analytic Varieties A Geometric Interpretation of the GSV Index Topological Invariants and Curvatura Integra Relation with the Milnor Number for Real Singularities The Virtual Index The Virtual Tangent Bundle of a Local Complete Intersection Chern Weil Theory for Virtual Bundles Characteristic Numbers on Singular Varieties The Virtual Index Identification with GSV Index When Singularities are Isolated A Generalization of the Adjunction Formula An Integral Formula for the Virtual Index The Case of Holomorphic Vector Fields Baum Bott Residues of Holomorphic Vector Fields One-Dimensional Singular Foliations Residues of Holomorphic Vector Fields on Singular Varieties Grothendieck Residues Relative to a Subvariety Residues for the Ambient Tangent Bundle (Generalized Variation) Residues for the Normal Bundle (Residues of Type Camacho Sad) Residues for the Virtual Tangent Bundle (Singular Baum Bott)
4 Contents xi 7 The Homological Index and Algebraic Formulas The Homological Index The Hypersurface Case The Index of Real Analytic Vector Fields The Signature Formula of Eisenbud Levine Khimshiashvili The Index on Real Hypersurface Singularities The Local Euler Obstruction Definition of the Euler Obstruction. The Nash Blow Up Proportionality Theorem for Vector Fields Euler Obstruction and Hyperplane Sections The Local Euler Obstruction of a Function The Euler Obstruction and the Euler Defect The Euler Defect at General Points The Euler Obstruction via Morse Theory Indices for 1-Forms Some Basic Facts About 1-Forms Radial Extension and the Schwartz Index Local Euler Obstruction of a 1-Form and the Proportionality Theorem The Radial Index The GSV Index Isolated Singularity Case Nonisolated Singularity Case The Homological Index On the Milnor Number of an Isolated Singularity Indices for Collections of 1-Forms The GSV Index for Collections of 1-Forms Local Chern Obstructions The Schwartz Classes The Local Schwartz Index of a Frame Proportionality Theorem The Schwartz Classes Alexander and Other Homomorphisms Localization of the Schwartz Classes The Topological Viewpoint The Differential Geometric Viewpoint MacPherson and Mather Classes
5 xii Contents 11 The Virtual Classes Virtual Classes Lifting a Frame to the Milnor Fiber The Fulton Johnson Classes Localization of the Virtual Classes Milnor Number and Milnor Classes Milnor Classes Localization of Milnor Classes Differential Geometric Point of View Generalized Milnor Number Characteristic Classes of Coherent Sheaves on Singular Varieties Local Chern Classes and Characters in the Čech-de Rham Cohomology Thom Class Riemann-Roch Theorem for Embeddings Homology Chern Characters and Classes Characteristic Classes of the Tangent Sheaf References Index
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