Manifolds, Sheaves, and Cohomology
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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2 Algebraic Topological Preliminaries
5 Linearization of Manifolds
6 Lie Groups
7 Torsors and Nonabelian Čech Cohomology
11 Cohomology of Constant Sheaves
The Language of Categories
9 Soft Sheaves
10 Cohomology of Complexes of Sheaves