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.

Table of Contents

1 Topological Preliminaries

2 Algebraic Topological Preliminaries

3 Sheaves

4 Manifolds

5 Linearization of Manifolds

6 Lie Groups

7 Torsors and Non-abelian Cech Cohomology

8 Bundles

9 Soft Sheaves

1 O Cohomology of Complexes of Sheaves

11 Cohomology of Constant Sheaves

12 Appendix A: Basic Topology

13 Appendix B: The l anguage of Categories

14 Appendix C: Basic Algebra

15 Appendix D: Homological Algebra

16 Appendix E: local Analysis

About the Author

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