Manifolds, Sheaves, and Cohomology (Springer Studium Mathematik – Master) by Torsten Wedhorn (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review “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) From the Back Cover 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.ContentTopological 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 AnalysisReadershipGraduate Students in Mathematics / Master of Science in Mathematics About the AuthorProf. Dr. Torsten Wedhorn, Department of Mathematics, Technische Universität Darmstadt, Germany About the Author Prof. Dr. Torsten Wedhorn, Department of Mathematics, Technische Universität Darmstadt, Germany Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The book was good but the delivery was late

⭐Finally, we have a well-written book which consistently adopts the ringed space approach to manifolds.One cannot overstate the need for such a text. Thank you Torsten Wedhorn.

⭐I started getting interested in Sheaf Theory a few months ago, and I found it really hard, since most of the books just give some definitions and a few theorems, without many comments or examples, and with very sketchy proofs. I then tried Tennison’s “Sheaf Theory”, which is much more detailed, but “old” in notations, so not always readable.”Manifolds, Sheaves, and Cohomology” is definitely the best book I’ve found so far. It is incredibly readable, with lots of examples and many useful remarks. Every proof is very detailed, and every background information you may need is included in the 5 appendices (Basic Topology, The Language of Categories, Basic Algebra, Homological Algebra, Local Analysis). Furthermore, the layout is great and the book easily stays open, so it is really a pleasure to read it.This book does not go that deep in the study of sheaf theory, but everything is clear and simple. I would truly like any professor to follow it in their sheaf theory classes for graduate students. I also recommend anyone who finds this subject hard (just like me) to give this book a try.

⭐Gibt einen umfassenden Überblick über Mannigfaltigkeiten, Garben und ihre Topologie.

⭐

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