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.

Provides a modern introduction to the theory of manifolds Offers a good preparation for more advanced geometric theories A novel approach for master students in mathematics Includes supplementary material: sn.pub/extras

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. <p