Advertisement

© 2016

Manifolds, Sheaves, and Cohomology

Textbook

Part of the Springer Studium Mathematik - Master book series (SSMM)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Torsten Wedhorn
    Pages 1-20
  3. Torsten Wedhorn
    Pages 21-40
  4. Torsten Wedhorn
    Pages 41-68
  5. Torsten Wedhorn
    Pages 69-90
  6. Torsten Wedhorn
    Pages 91-121
  7. Torsten Wedhorn
    Pages 123-137
  8. Torsten Wedhorn
    Pages 139-151
  9. Torsten Wedhorn
    Pages 153-192
  10. Torsten Wedhorn
    Pages 193-204
  11. Torsten Wedhorn
    Pages 205-232
  12. Torsten Wedhorn
    Pages 233-244
  13. Torsten Wedhorn
    Pages 245-269
  14. Torsten Wedhorn
    Pages 271-290
  15. Torsten Wedhorn
    Pages 291-315
  16. Torsten Wedhorn
    Pages 317-330
  17. Torsten Wedhorn
    Pages 331-340
  18. Back Matter
    Pages 341-354

About this book

Introduction

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

Keywords

Bundles Cohomology Lie Groups Manifolds Sheaves

Authors and affiliations

  1. 1.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany

About the authors

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

Bibliographic information

Reviews

“This book is to introduce powerful techniques used in modern Algebraic and Differential Geometry, fundamentally focusing on the relation between local and global properties of geometric objects and on the obstructions to passing from the former to the latter. … The readership for this book will mostly consist of beginner to intermediate graduate students, and it may serve as the basis for a one-semester course on the cohomology of sheaves and its relation to real and complex manifolds.” (Rui Miguel Saramago, zbMATH 1361.55001, 2017)