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.ContentTopological 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 AnalysisReadershipGraduate Students in Mathematics / Master of Science in Mathematics About the AuthorProf. Dr. Torsten Wedhorn, Department of Mathematics, Technische Universität Darmstadt, Germany

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.