Manifolds, Sheaves, and Cohomology

ISBN-13: 9783658106324 / Angielski / Miękka / 2016 / 354 str.

Torsten Wedhorn

Opis

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.

Recenzje

"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)

Spis treści

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.

O autorze

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

Blurb

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