Author: Dagmar M. Meyer
Publisher: Cambridge University Press
ISBN: 9780521850643
Category : Mathematics
Languages : en
Pages : 210
Book Description
A monograph demonstrating remarkable and unexpected interdisciplinary connections in the areas of commutative algebra, invariant theory and algebraic topology.
Poincaré Duality Algebras, Macaulay's Dual Systems, and Steenrod Operations
Author: Dagmar M. Meyer
Publisher: Cambridge University Press
ISBN: 9780521850643
Category : Mathematics
Languages : en
Pages : 210
Book Description
A monograph demonstrating remarkable and unexpected interdisciplinary connections in the areas of commutative algebra, invariant theory and algebraic topology.
Publisher: Cambridge University Press
ISBN: 9780521850643
Category : Mathematics
Languages : en
Pages : 210
Book Description
A monograph demonstrating remarkable and unexpected interdisciplinary connections in the areas of commutative algebra, invariant theory and algebraic topology.
Equivariant Poincaré Duality on G-Manifolds
Author: Alberto Arabia
Publisher: Springer Nature
ISBN: 3030704408
Category : Mathematics
Languages : en
Pages : 383
Book Description
This book carefully presents a unified treatment of equivariant Poincaré duality in a wide variety of contexts, illuminating an area of mathematics that is often glossed over elsewhere. The approach used here allows the parallel treatment of both equivariant and nonequivariant cases. It also makes it possible to replace the usual field of coefficients for cohomology, the field of real numbers, with any field of arbitrary characteristic, and hence change (equivariant) de Rham cohomology to the usual singular (equivariant) cohomology . The book will be of interest to graduate students and researchers wanting to learn about the equivariant extension of tools familiar from non-equivariant differential geometry.
Publisher: Springer Nature
ISBN: 3030704408
Category : Mathematics
Languages : en
Pages : 383
Book Description
This book carefully presents a unified treatment of equivariant Poincaré duality in a wide variety of contexts, illuminating an area of mathematics that is often glossed over elsewhere. The approach used here allows the parallel treatment of both equivariant and nonequivariant cases. It also makes it possible to replace the usual field of coefficients for cohomology, the field of real numbers, with any field of arbitrary characteristic, and hence change (equivariant) de Rham cohomology to the usual singular (equivariant) cohomology . The book will be of interest to graduate students and researchers wanting to learn about the equivariant extension of tools familiar from non-equivariant differential geometry.
Poincare Duality in Homology Manifolds
Author: Frank Albert Raymond
Publisher:
ISBN:
Category : Homology theory
Languages : en
Pages : 164
Book Description
Publisher:
ISBN:
Category : Homology theory
Languages : en
Pages : 164
Book Description
History of Topology
Author: I.M. James
Publisher: Elsevier
ISBN: 0080534074
Category : Mathematics
Languages : en
Pages : 1067
Book Description
Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincaré who "gave topology wings" in a classic series of articles published around the turn of the century. While the earlier history, sometimes called the prehistory, is also considered, this volume is mainly concerned with the more recent history of topology, from Poincaré onwards.As will be seen from the list of contents the articles cover a wide range of topics. Some are more technical than others, but the reader without a great deal of technical knowledge should still find most of the articles accessible. Some are written by professional historians of mathematics, others by historically-minded mathematicians, who tend to have a different viewpoint.
Publisher: Elsevier
ISBN: 0080534074
Category : Mathematics
Languages : en
Pages : 1067
Book Description
Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincaré who "gave topology wings" in a classic series of articles published around the turn of the century. While the earlier history, sometimes called the prehistory, is also considered, this volume is mainly concerned with the more recent history of topology, from Poincaré onwards.As will be seen from the list of contents the articles cover a wide range of topics. Some are more technical than others, but the reader without a great deal of technical knowledge should still find most of the articles accessible. Some are written by professional historians of mathematics, others by historically-minded mathematicians, who tend to have a different viewpoint.
Cohomology of Groups
Author: Kenneth S. Brown
Publisher: Springer Science & Business Media
ISBN: 9780387906881
Category : Mathematics
Languages : en
Pages : 322
Book Description
Aimed at second year graduate students, this text introduces them to cohomology theory (involving a rich interplay between algebra and topology) with a minimum of prerequisites. No homological algebra is assumed beyond what is normally learned in a first course in algebraic topology, and the basics of the subject, as well as exercises, are given prior to discussion of more specialized topics.
Publisher: Springer Science & Business Media
ISBN: 9780387906881
Category : Mathematics
Languages : en
Pages : 322
Book Description
Aimed at second year graduate students, this text introduces them to cohomology theory (involving a rich interplay between algebra and topology) with a minimum of prerequisites. No homological algebra is assumed beyond what is normally learned in a first course in algebraic topology, and the basics of the subject, as well as exercises, are given prior to discussion of more specialized topics.
Geometry, Topology and Physics, Second Edition
Author: Mikio Nakahara
Publisher: CRC Press
ISBN: 9780750306065
Category : Mathematics
Languages : en
Pages : 598
Book Description
Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields. The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology. The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory. Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics. The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view. Geometry, Topology and Physics, Second Edition is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics.
Publisher: CRC Press
ISBN: 9780750306065
Category : Mathematics
Languages : en
Pages : 598
Book Description
Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields. The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology. The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory. Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics. The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view. Geometry, Topology and Physics, Second Edition is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics.
Algebraic Topology
Author: C. R. F. Maunder
Publisher: Cambridge University Press
ISBN: 9780521298407
Category : Mathematics
Languages : en
Pages : 392
Book Description
Based on lectures to advanced undergraduate and first-year graduate students, this is a thorough, sophisticated, and modern treatment of elementary algebraic topology, essentially from a homotopy theoretic viewpoint. Author C.R.F. Maunder provides examples and exercises; and notes and references at the end of each chapter trace the historical development of the subject. Copyright © Libri GmbH. All rights reserved.
Publisher: Cambridge University Press
ISBN: 9780521298407
Category : Mathematics
Languages : en
Pages : 392
Book Description
Based on lectures to advanced undergraduate and first-year graduate students, this is a thorough, sophisticated, and modern treatment of elementary algebraic topology, essentially from a homotopy theoretic viewpoint. Author C.R.F. Maunder provides examples and exercises; and notes and references at the end of each chapter trace the historical development of the subject. Copyright © Libri GmbH. All rights reserved.
Poincare Duality Spaces
Author: Oliver Lee Costich
Publisher:
ISBN:
Category : Homology theory
Languages : en
Pages : 102
Book Description
Publisher:
ISBN:
Category : Homology theory
Languages : en
Pages : 102
Book Description
Orbifolds and Stringy Topology
Author: Alejandro Adem
Publisher: Cambridge University Press
ISBN: 1139464485
Category : Mathematics
Languages : en
Pages : 138
Book Description
An introduction to the theory of orbifolds from a modern perspective, combining techniques from geometry, algebraic topology and algebraic geometry. One of the main motivations, and a major source of examples, is string theory, where orbifolds play an important role. The subject is first developed following the classical description analogous to manifold theory, after which the book branches out to include the useful description of orbifolds provided by groupoids, as well as many examples in the context of algebraic geometry. Classical invariants such as de Rham cohomology and bundle theory are developed, a careful study of orbifold morphisms is provided, and the topic of orbifold K-theory is covered. The heart of this book, however, is a detailed description of the Chen-Ruan cohomology, which introduces a product for orbifolds and has had significant impact. The final chapter includes explicit computations for a number of interesting examples.
Publisher: Cambridge University Press
ISBN: 1139464485
Category : Mathematics
Languages : en
Pages : 138
Book Description
An introduction to the theory of orbifolds from a modern perspective, combining techniques from geometry, algebraic topology and algebraic geometry. One of the main motivations, and a major source of examples, is string theory, where orbifolds play an important role. The subject is first developed following the classical description analogous to manifold theory, after which the book branches out to include the useful description of orbifolds provided by groupoids, as well as many examples in the context of algebraic geometry. Classical invariants such as de Rham cohomology and bundle theory are developed, a careful study of orbifold morphisms is provided, and the topic of orbifold K-theory is covered. The heart of this book, however, is a detailed description of the Chen-Ruan cohomology, which introduces a product for orbifolds and has had significant impact. The final chapter includes explicit computations for a number of interesting examples.
POINCARE DUALITY IN HOMOLOGY MANIFOLDS.
Author: FRANK ALBERT RAYMOND
Publisher:
ISBN:
Category :
Languages : en
Pages : 164
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 164
Book Description