Manifolds, Sheaves, and Cohomology

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Springer, Jul 25, 2016 - Mathematics - 354 pages

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.

 

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Contents

1 Topological Preliminaries
1
2 Algebraic Topological Preliminaries
21
3 Sheaves
41
4 Manifolds
69
5 Linearization of Manifolds
91
6 Lie Groups
123
7 Torsors and Nonabelian Čech Cohomology
138
8 Bundles
153
11 Cohomology of Constant Sheaves
233
Basic Topology
245
The Language of Categories
270
Basic Algebra
291
Homological Algebra
317
Local Analysis
331
References
341
Index
343

9 Soft Sheaves
193
10 Cohomology of Complexes of Sheaves
205

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About the author (2016)

Prof. Dr. Torsten Wedhorn, Department of Mathematics, Technische Universitńt Darmstadt, Germany