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Manifolds, Sheaves, and Cohomology

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This book explains techniques that are essential in almost all branches of modern geometry such as algebraic geometry, complex geometry, or non-archimedian geometry. It uses the most accessible case, real and complex manifolds, as a model. The author especially emphasizes the difference between local and global questions. Cohomology theory of sheaves is introduced and its usage is illustrated by many examples.

Author(s): Torsten Wedhorn
Series: Springer Studium Mathematik
Publisher: Springer
Year: 2016

Language: English
Pages: 366
Tags: Category Theory, Homological Algebra;Topological Groups, Lie Groups;Differential Geometry;Global Analysis and Analysis on Manifolds

Front Matter....Pages i-xvi
Topological Preliminaries....Pages 1-20
Algebraic Topological Preliminaries....Pages 21-40
Sheaves....Pages 41-68
Manifolds....Pages 69-90
Linearization of Manifolds....Pages 91-121
Lie Groups....Pages 123-137
Torsors and Non-abelian \Čech Cohomology....Pages 139-151
Bundles....Pages 153-192
Soft Sheaves....Pages 193-204
Cohomology of Complexes of Sheaves....Pages 205-232
Cohomology of Constant Sheaves....Pages 233-244
Appendix A: Basic Topology....Pages 245-269
Appendix B: The Language of Categories....Pages 271-290
Appendix C: Basic Algebra....Pages 291-315
Appendix D: Homological Algebra....Pages 317-330
Appendix E: Local Analysis....Pages 331-340
Back Matter....Pages 341-354