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.

Content Topological Preliminaries - Algebraic Topological Preliminaries - Sheaves - Manifolds - Local Theory of Manifolds - Lie Groups - Torsors and Non-abelian Cech Cohomology - Bundles - Soft Sheaves - Cohomology of Complexes of Sheaves - Cohomology of Sheaves of Locally Constant Functions - Appendix: Basic Topology, The Language of Categories, Basic Algebra, Homological Algebra, Local Analysis

Readership Graduate Students in Mathematics / Master of Science in Mathematics

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

Autorentext

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

Inhalt

Topological Preliminaries.- Algebraic Topological Preliminaries.- Sheaves.- Manifolds.- Local Theory of Manifolds.- Lie Groups.- Torsors and Non-abelian Cech Cohomology.- Bundles.- Soft Sheaves.- Cohomology of Complexes of Sheaves.- Cohomology of Sheaves of Locally Constant Functions.- Appendix: Basic Topology, The Language of Categories, Basic Algebra, Homological Algebra, Local Analysis.