Homology, Cohomology, And Sheaf Cohomology For Algebraic Topology, Algebraic Geometry, And Differential Geometry

Homology, Cohomology, And Sheaf Cohomology For Algebraic Topology, Algebraic Geometry, And Differential Geometry
Title Homology, Cohomology, And Sheaf Cohomology For Algebraic Topology, Algebraic Geometry, And Differential Geometry PDF eBook
Author Jean H Gallier
Publisher World Scientific
Pages 799
Release 2022-01-19
Genre Mathematics
ISBN 9811245045

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For more than thirty years the senior author has been trying to learn algebraic geometry. In the process he discovered that many of the classic textbooks in algebraic geometry require substantial knowledge of cohomology, homological algebra, and sheaf theory. In an attempt to demystify these abstract concepts and facilitate understanding for a new generation of mathematicians, he along with co-author wrote this book for an audience who is familiar with basic concepts of linear and abstract algebra, but who never has had any exposure to the algebraic geometry or homological algebra. As such this book consists of two parts. The first part gives a crash-course on the homological and cohomological aspects of algebraic topology, with a bias in favor of cohomology. The second part is devoted to presheaves, sheaves, Cech cohomology, derived functors, sheaf cohomology, and spectral sequences. All important concepts are intuitively motivated and the associated proofs of the quintessential theorems are presented in detail rarely found in the standard texts.

Homology, Cohomology, and Sheaf Cohomology for Algebraic Topology, Algebraic Geometry, and Differential Geometry

Homology, Cohomology, and Sheaf Cohomology for Algebraic Topology, Algebraic Geometry, and Differential Geometry
Title Homology, Cohomology, and Sheaf Cohomology for Algebraic Topology, Algebraic Geometry, and Differential Geometry PDF eBook
Author Jean H. Gallier
Publisher
Pages 0
Release 2022
Genre Algebraic topology
ISBN 9789811245039

Download Homology, Cohomology, and Sheaf Cohomology for Algebraic Topology, Algebraic Geometry, and Differential Geometry Book in PDF, Epub and Kindle

"For more than thirty years the senior author has been trying to learn algebraic geometry. In the process he discovered that many of the classic textbooks in algebraic geometry require substantial knowledge of cohomology, homological algebra, and sheaf theory. In an attempt to demystify these abstract concepts and facilitate understanding for a new generation of mathematicians, he along with co-author wrote this book for an audience who is familiar with basic concepts of linear and abstract algebra, but who never has had any exposure to the algebraic geometry or homological algebra. As such this book consists of two parts. The first part gives a crash-course on the homological and cohomological aspects of algebraic topology, with a bias in favor of cohomology. The second part is devoted to presheaves, sheaves, Cech cohomology, derived functors, sheaf cohomology, and spectral sequences. All important concepts are intuitively motivated and the associated proofs of the quintessential theorems are presented in detail rarely found in the standard texts"--

Algebraic Topology

Algebraic Topology
Title Algebraic Topology PDF eBook
Author Andrew H. Wallace
Publisher Courier Corporation
Pages 290
Release 2007-01-01
Genre Mathematics
ISBN 0486462390

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Surveys several algebraic invariants, including the fundamental group, singular and Cech homology groups, and a variety of cohomology groups.

Differential Forms in Algebraic Topology

Differential Forms in Algebraic Topology
Title Differential Forms in Algebraic Topology PDF eBook
Author Raoul Bott
Publisher Springer Science & Business Media
Pages 319
Release 2013-04-17
Genre Mathematics
ISBN 1475739516

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Developed from a first-year graduate course in algebraic topology, this text is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas: de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes. By using the de Rham theory of differential forms as a prototype of cohomology, the machineries of algebraic topology are made easier to assimilate. With its stress on concreteness, motivation, and readability, this book is equally suitable for self-study and as a one-semester course in topology.

Algebraic Topology Via Differential Geometry

Algebraic Topology Via Differential Geometry
Title Algebraic Topology Via Differential Geometry PDF eBook
Author M. Karoubi
Publisher Cambridge University Press
Pages 380
Release 1987
Genre Mathematics
ISBN 9780521317146

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In this volume the authors seek to illustrate how methods of differential geometry find application in the study of the topology of differential manifolds. Prerequisites are few since the authors take pains to set out the theory of differential forms and the algebra required. The reader is introduced to De Rham cohomology, and explicit and detailed calculations are present as examples. Topics covered include Mayer-Vietoris exact sequences, relative cohomology, Pioncare duality and Lefschetz's theorem. This book will be suitable for graduate students taking courses in algebraic topology and in differential topology. Mathematicians studying relativity and mathematical physics will find this an invaluable introduction to the techniques of differential geometry.

Homology Theory

Homology Theory
Title Homology Theory PDF eBook
Author James W. Vick
Publisher Springer Science & Business Media
Pages 258
Release 2012-12-06
Genre Mathematics
ISBN 1461208815

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This introduction to some basic ideas in algebraic topology is devoted to the foundations and applications of homology theory. After the essentials of singular homology and some important applications are given, successive topics covered include attaching spaces, finite CW complexes, cohomology products, manifolds, Poincare duality, and fixed point theory. This second edition includes a chapter on covering spaces and many new exercises.

Basic Algebraic Topology

Basic Algebraic Topology
Title Basic Algebraic Topology PDF eBook
Author Anant R. Shastri
Publisher CRC Press
Pages 552
Release 2016-02-03
Genre Mathematics
ISBN 1466562447

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Building on rudimentary knowledge of real analysis, point-set topology, and basic algebra, Basic Algebraic Topology provides plenty of material for a two-semester course in algebraic topology. The book first introduces the necessary fundamental concepts, such as relative homotopy, fibrations and cofibrations, category theory, cell complexes, and si