Manifolds, Sheaves, and Cohomology

Description

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. 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