Manifolds, Sheaves, and Cohomology

Torsten Wedhorn

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English

Springer Spektrum
03 August 2016

Groups & group theory; Calculus & mathematical analysis; Differential & Riemannian geometry

Series: Springer Studium Mathematik - Master

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.

By: Torsten Wedhorn
Imprint: Springer Spektrum
Country of Publication: Germany
Edition: 1st ed. 2016
Dimensions: Height: 240mm, Width: 168mm, Spine: 20mm
Weight: 6.221kg
ISBN: 9783658106324
ISBN 10: 3658106328
Series: Springer Studium Mathematik - Master
Pages: 354
Publication Date: 03 August 2016
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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.

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

Reviews for Manifolds, Sheaves, and Cohomology

“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)