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

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

Jean H Gallier,Jocelyn Quaintance
Homology Cohomology And Sheaf Cohomology For Algebraic Topology Algebraic Geometry And Differential Geometry Book PDF

Author : Jean H Gallier,Jocelyn Quaintance
Publisher : World Scientific
Page : 799 pages
File Size : 42,9 Mb
Release : 2022-01-19
Category : Mathematics
ISBN : 9789811245046

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Homology, Cohomology, And Sheaf Cohomology For Algebraic Topology, Algebraic Geometry, And Differential Geometry by Jean H Gallier,Jocelyn Quaintance Pdf

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

Jean H. Gallier,Jocelyn Quaintance
Homology Cohomology and Sheaf Cohomology for Algebraic Topology Algebraic Geometry and Differential Geometry Book PDF

Author : Jean H. Gallier,Jocelyn Quaintance
Publisher : Unknown
Page : 0 pages
File Size : 49,9 Mb
Release : 2022
Category : Algebraic topology
ISBN : 9811245037

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Homology, Cohomology, and Sheaf Cohomology for Algebraic Topology, Algebraic Geometry, and Differential Geometry by Jean H. Gallier,Jocelyn Quaintance Pdf

"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

Andrew H. Wallace
Algebraic Topology Book PDF

Author : Andrew H. Wallace
Publisher : Courier Corporation
Page : 290 pages
File Size : 40,8 Mb
Release : 2007-01-01
Category : Mathematics
ISBN : 9780486462394

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Algebraic Topology by Andrew H. Wallace Pdf

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

A Geometric Approach to Homology Theory

S. Buoncristiano,Colin Patrick Rourke,Brian Joseph Sanderson
A Geometric Approach to Homology Theory Book PDF

Author : S. Buoncristiano,Colin Patrick Rourke,Brian Joseph Sanderson
Publisher : Cambridge University Press
Page : 157 pages
File Size : 44,9 Mb
Release : 1976-04
Category : Mathematics
ISBN : 9780521209403

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A Geometric Approach to Homology Theory by S. Buoncristiano,Colin Patrick Rourke,Brian Joseph Sanderson Pdf

The purpose of these notes is to give a geometrical treatment of generalized homology and cohomology theories. The central idea is that of a 'mock bundle', which is the geometric cocycle of a general cobordism theory, and the main new result is that any homology theory is a generalized bordism theory. The book will interest mathematicians working in both piecewise linear and algebraic topology especially homology theory as it reaches the frontiers of current research in the topic. The book is also suitable for use as a graduate course in homology theory.

Sheaf Theory

Glen E. Bredon
Sheaf Theory Book PDF

Author : Glen E. Bredon
Publisher : Springer Science & Business Media
Page : 518 pages
File Size : 48,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461206477

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Sheaf Theory by Glen E. Bredon Pdf

Primarily concerned with the study of cohomology theories of general topological spaces with "general coefficient systems", the parts of sheaf theory covered here are those areas important to algebraic topology. Among the many innovations in this book, the concept of the "tautness" of a subspace is introduced and exploited; the fact that sheaf theoretic cohomology satisfies the homotopy property is proved for general topological spaces; and relative cohomology is introduced into sheaf theory. A list of exercises at the end of each chapter helps students to learn the material, and solutions to many of the exercises are given in an appendix. This new edition of a classic has been substantially rewritten and now includes some 80 additional examples and further explanatory material, as well as new sections on Cech cohomology, the Oliver transfer, intersection theory, generalised manifolds, locally homogeneous spaces, homological fibrations and p- adic transformation groups. Readers should have a thorough background in elementary homological algebra and in algebraic topology.

Intersection Cohomology

Armand Borel
Intersection Cohomology Book PDF

Author : Armand Borel
Publisher : Springer Science & Business Media
Page : 242 pages
File Size : 55,9 Mb
Release : 2008-01-21
Category : Mathematics
ISBN : 9780817647643

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Intersection Cohomology by Armand Borel Pdf

This book is a publication in Swiss Seminars, a subseries of Progress in Mathematics. It is an expanded version of the notes from a seminar on intersection cohomology theory, which met at the University of Bern, Switzerland, in the spring of 1983. This volume supplies an introduction to the piecewise linear and sheaf-theoretic versions of that theory as developed by M. Goresky and R. MacPherson in Topology 19 (1980), and in Inventiones Mathematicae 72 (1983). Some familiarity with algebraic topology and sheaf theory is assumed.

Homological Algebra

S.I. Gelfand,Yu.I. Manin
Homological Algebra Book PDF

Author : S.I. Gelfand,Yu.I. Manin
Publisher : Springer Science & Business Media
Page : 229 pages
File Size : 49,8 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783642579110

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Homological Algebra by S.I. Gelfand,Yu.I. Manin Pdf

This book, the first printing of which was published as volume 38 of the Encyclopaedia of Mathematical Sciences, presents a modern approach to homological algebra, based on the systematic use of the terminology and ideas of derived categories and derived functors. The book contains applications of homological algebra to the theory of sheaves on topological spaces, to Hodge theory, and to the theory of modules over rings of algebraic differential operators (algebraic D-modules). The authors Gelfand and Manin explain all the main ideas of the theory of derived categories. Both authors are well-known researchers and the second, Manin, is famous for his work in algebraic geometry and mathematical physics. The book is an excellent reference for graduate students and researchers in mathematics and also for physicists who use methods from algebraic geometry and algebraic topology.

Homology Theory

James W. Vick
Homology Theory Book PDF

Author : James W. Vick
Publisher : Springer Science & Business Media
Page : 258 pages
File Size : 49,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461208815

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Homology Theory by James W. Vick Pdf

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.

Homological Algebra

S.I. Gelfand,Yu.I. Manin
Homological Algebra Book PDF

Author : S.I. Gelfand,Yu.I. Manin
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 44,6 Mb
Release : 1994-03-29
Category : Mathematics
ISBN : 3540533737

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Homological Algebra by S.I. Gelfand,Yu.I. Manin Pdf

This book, the first printing of which was published as volume 38 of the Encyclopaedia of Mathematical Sciences, presents a modern approach to homological algebra, based on the systematic use of the terminology and ideas of derived categories and derived functors. The book contains applications of homological algebra to the theory of sheaves on topological spaces, to Hodge theory, and to the theory of modules over rings of algebraic differential operators (algebraic D-modules). The authors Gelfand and Manin explain all the main ideas of the theory of derived categories. Both authors are well-known researchers and the second, Manin, is famous for his work in algebraic geometry and mathematical physics. The book is an excellent reference for graduate students and researchers in mathematics and also for physicists who use methods from algebraic geometry and algebraic topology.

Intersection Homology & Perverse Sheaves

Laurenţiu G. Maxim
Intersection Homology Perverse Sheaves Book PDF

Author : Laurenţiu G. Maxim
Publisher : Springer Nature
Page : 270 pages
File Size : 52,9 Mb
Release : 2019-11-30
Category : Mathematics
ISBN : 9783030276447

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Intersection Homology & Perverse Sheaves by Laurenţiu G. Maxim Pdf

This textbook provides a gentle introduction to intersection homology and perverse sheaves, where concrete examples and geometric applications motivate concepts throughout. By giving a taste of the main ideas in the field, the author welcomes new readers to this exciting area at the crossroads of topology, algebraic geometry, analysis, and differential equations. Those looking to delve further into the abstract theory will find ample references to facilitate navigation of both classic and recent literature. Beginning with an introduction to intersection homology from a geometric and topological viewpoint, the text goes on to develop the sheaf-theoretical perspective. Then algebraic geometry comes to the fore: a brief discussion of constructibility opens onto an in-depth exploration of perverse sheaves. Highlights from the following chapters include a detailed account of the proof of the Beilinson–Bernstein–Deligne–Gabber (BBDG) decomposition theorem, applications of perverse sheaves to hypersurface singularities, and a discussion of Hodge-theoretic aspects of intersection homology via Saito’s deep theory of mixed Hodge modules. An epilogue offers a succinct summary of the literature surrounding some recent applications. Intersection Homology & Perverse Sheaves is suitable for graduate students with a basic background in topology and algebraic geometry. By building context and familiarity with examples, the text offers an ideal starting point for those entering the field. This classroom-tested approach opens the door to further study and to current research.

Basic Algebraic Topology

Anant R. Shastri
Basic Algebraic Topology Book PDF

Author : Anant R. Shastri
Publisher : CRC Press
Page : 552 pages
File Size : 43,5 Mb
Release : 2016-02-03
Category : Mathematics
ISBN : 9781466562448

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Basic Algebraic Topology by Anant R. Shastri Pdf

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

Manifolds, Sheaves, and Cohomology

Torsten Wedhorn
Manifolds Sheaves and Cohomology Book PDF

Author : Torsten Wedhorn
Publisher : Springer
Page : 366 pages
File Size : 51,9 Mb
Release : 2016-07-25
Category : Mathematics
ISBN : 9783658106331

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Manifolds, Sheaves, and Cohomology by Torsten Wedhorn Pdf

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.

Algebraic Topology

Edwin H. Spanier
Algebraic Topology Book PDF

Author : Edwin H. Spanier
Publisher : Springer Science & Business Media
Page : 502 pages
File Size : 50,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468493221

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Algebraic Topology by Edwin H. Spanier Pdf

This book surveys the fundamental ideas of algebraic topology. The first part covers the fundamental group, its definition and application in the study of covering spaces. The second part turns to homology theory including cohomology, cup products, cohomology operations and topological manifolds. The final part is devoted to Homotropy theory, including basic facts about homotropy groups and applications to obstruction theory.

Differential Forms in Algebraic Topology

Raoul Bott,Loring W. Tu
Differential Forms in Algebraic Topology Book PDF

Author : Raoul Bott,Loring W. Tu
Publisher : Springer Science & Business Media
Page : 319 pages
File Size : 50,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475739510

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Differential Forms in Algebraic Topology by Raoul Bott,Loring W. Tu Pdf

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 Geometry II

I.R. Shafarevich
Algebraic Geometry II Book PDF

Author : I.R. Shafarevich
Publisher : Springer Science & Business Media
Page : 282 pages
File Size : 48,5 Mb
Release : 1995-12-21
Category : Mathematics
ISBN : 3540546804

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Algebraic Geometry II by I.R. Shafarevich Pdf

This two-part volume contains numerous examples and insights on various topics. The authors have taken pains to present the material rigorously and coherently. This book will be immensely useful to mathematicians and graduate students working in algebraic geometry, arithmetic algebraic geometry, complex analysis and related fields.