Manifolds, Sheaves, and Cohomology

• Main Author: Wedhorn, Torsten (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Wiesbaden : Springer Fachmedien Wiesbaden : Imprint: Springer Spektrum, 2016.
• Series: Springer Studium Mathematik - Master
• Subjects: Mathematics.; Category theory (Mathematics).; Homological algebra.; Topological groups.; Lie groups.; Global analysis (Mathematics).; Manifolds (Mathematics).; Differential geometry.; Category Theory, Homological Algebra.; Topological Groups, Lie Groups.; Differential Geometry.; Global Analysis and Analysis on Manifolds.

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 loca...

Table of Contents:

• 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.