A History Of Algebraic And Differential Topology 1900 1960
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A History Of Algebraic And Differential Topology 1900 1960
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Author : Jean Dieudonné
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-09-01
A History Of Algebraic And Differential Topology 1900 1960 written by Jean Dieudonné and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-01 with Mathematics categories.
This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincaré and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results.... Within its chosen boundaries the coverage of this book is superb. Read it! —MathSciNet
A History Of Algebraic And Differential Topology 1900 1960
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Author : Jean Dieudonné
language : en
Publisher: Birkhäuser
Release Date : 2009-06-09
A History Of Algebraic And Differential Topology 1900 1960 written by Jean Dieudonné and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-09 with Mathematics categories.
This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincaré and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results.... Within its chosen boundaries the coverage of this book is superb. Read it! —MathSciNet
History Of Algebraic And Differential Topology 1900 1960
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Author : J. Dieudonné
language : en
Publisher:
Release Date : 1994
History Of Algebraic And Differential Topology 1900 1960 written by J. Dieudonné and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.
Real Algebraic Differential Topology
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Author : Richard S. Palais
language : en
Publisher:
Release Date : 1981
Real Algebraic Differential Topology written by Richard S. Palais and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.
History Of Topology
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Author : I.M. James
language : en
Publisher: Elsevier
Release Date : 1999-08-24
History Of Topology written by I.M. James and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-08-24 with Mathematics categories.
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.
Basic Algebraic Topology And Its Applications
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Author : Mahima Ranjan Adhikari
language : en
Publisher: Springer
Release Date : 2016-09-16
Basic Algebraic Topology And Its Applications written by Mahima Ranjan Adhikari and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-16 with Mathematics categories.
This book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book offers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. The book studies a variety of maps, which are continuous functions between spaces. It also reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to engage in further study.
Homology Theory
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Author : James W. Vick
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-01-07
Homology Theory written by James W. Vick and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-07 with Mathematics categories.
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.
Algebraic And Differential Topology
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Author : R.V. Gamkrelidze
language : en
Publisher: Routledge
Release Date : 2022-01-27
Algebraic And Differential Topology written by R.V. Gamkrelidze and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-27 with Mathematics categories.
Algebraic and Differential Topology presents in a clear, concise, and detailed manner the fundamentals of homology theory. It first defines the concept of a complex and its Betti groups, then discusses the topolgoical invariance of a Betti group. The book next presents various applications of homology theory, such as mapping of polyhedrons onto other polyhedrons as well as onto themselves. The third volume in L.S. Pontryagin's Selected Works, this book provides as many insights into algebraic topology for today's mathematician as it did when the author was making his initial endeavors into this field.
Basic Topology 2
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Author : Avishek Adhikari
language : en
Publisher: Springer Nature
Release Date : 2022-09-08
Basic Topology 2 written by Avishek Adhikari and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-08 with Mathematics categories.
This second of the three-volume book is targeted as a basic course in topology for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, algebra, and the theory of numbers. Offering a proper background on topology, analysis, and algebra, this volume discusses the topological groups and topological vector spaces that provide many interesting geometrical objects which relate algebra with geometry and analysis. This volume follows a systematic and comprehensive elementary approach to the topology related to manifolds, emphasizing differential topology. It further communicates the history of the emergence of the concepts leading to the development of topological groups, manifolds, and also Lie groups as mathematical topics with their motivations. This book will promote the scope, power, and active learning of the subject while covering a wide range of theories and applications in a balanced unified way.
An Introduction To Differential Manifolds
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Author : Jacques Lafontaine
language : en
Publisher: Springer
Release Date : 2015-07-29
An Introduction To Differential Manifolds written by Jacques Lafontaine and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-29 with Mathematics categories.
This book is an introduction to differential manifolds. It gives solid preliminaries for more advanced topics: Riemannian manifolds, differential topology, Lie theory. It presupposes little background: the reader is only expected to master basic differential calculus, and a little point-set topology. The book covers the main topics of differential geometry: manifolds, tangent space, vector fields, differential forms, Lie groups, and a few more sophisticated topics such as de Rham cohomology, degree theory and the Gauss-Bonnet theorem for surfaces. Its ambition is to give solid foundations. In particular, the introduction of “abstract” notions such as manifolds or differential forms is motivated via questions and examples from mathematics or theoretical physics. More than 150 exercises, some of them easy and classical, some others more sophisticated, will help the beginner as well as the more expert reader. Solutions are provided for most of them. The book should be of interest to various readers: undergraduate and graduate students for a first contact to differential manifolds, mathematicians from other fields and physicists who wish to acquire some feeling about this beautiful theory. The original French text Introduction aux variétés différentielles has been a best-seller in its category in France for many years. Jacques Lafontaine was successively assistant Professor at Paris Diderot University and Professor at the University of Montpellier, where he is presently emeritus. His main research interests are Riemannian and pseudo-Riemannian geometry, including some aspects of mathematical relativity. Besides his personal research articles, he was involved in several textbooks and research monographs.