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Manifolds, Sheaves, and Cohomology de Torsten Wedhorn

Manifolds, Sheaves, and Cohomology: Springer Studium Mathematik - Master

Autor Torsten Wedhorn
en Limba Engleză Paperback – 3 aug 2016
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.
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Specificații

ISBN-13: 9783658106324
ISBN-10: 3658106328
Pagini: 299
Ilustrații: XVI, 354 p. 9 illus.
Dimensiuni: 168 x 240 x 20 mm
Greutate: 0.59 kg
Ediția:1st ed. 2016
Editura: Springer Fachmedien Wiesbaden
Colecția Springer Spektrum
Seria Springer Studium Mathematik - Master

Locul publicării:Wiesbaden, Germany

Public țintă

Graduate

Cuprins

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.

Recenzii

“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)

Notă biografică

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

Textul de pe ultima copertă

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

Caracteristici

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