Algebraic And Differential Topology

Author : Jean Dieudonné
Publisher : Springer Science & Business Media
Page : 648 pages
File Size : 51,5 Mb
Release : 2009-09-01
Category : Mathematics
ISBN : 9780817649074

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A History of Algebraic and Differential Topology, 1900 - 1960 by Jean Dieudonné Pdf

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

Author : R. V. Gamkrelidze
Publisher : CRC Press
Page : 276 pages
File Size : 40,5 Mb
Release : 1987-03-06
Category : Mathematics
ISBN : 2881240356

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Algebraic and Differential Topology by R. V. Gamkrelidze Pdf

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.

Author : Raoul Bott,Loring W. Tu
Publisher : Springer Science & Business Media
Page : 319 pages
File Size : 53,5 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.

Author : Matthias Kreck
Publisher : American Mathematical Soc.
Page : 234 pages
File Size : 45,6 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821848982

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Differential Algebraic Topology by Matthias Kreck Pdf

This book presents a geometric introduction to the homology of topological spaces and the cohomology of smooth manifolds. The author introduces a new class of stratified spaces, so-called stratifolds. He derives basic concepts from differential topology such as Sard's theorem, partitions of unity and transversality. Based on this, homology groups are constructed in the framework of stratifolds and the homology axioms are proved. This implies that for nice spaces these homology groups agree with ordinary singular homology. Besides the standard computations of homology groups using the axioms, straightforward constructions of important homology classes are given. The author also defines stratifold cohomology groups following an idea of Quillen. Again, certain important cohomology classes occur very naturally in this description, for example, the characteristic classes which are constructed in the book and applied later on. One of the most fundamental results, Poincare duality, is almost a triviality in this approach. Some fundamental invariants, such as the Euler characteristic and the signature, are derived from (co)homology groups. These invariants play a significant role in some of the most spectacular results in differential topology. In particular, the author proves a special case of Hirzebruch's signature theorem and presents as a highlight Milnor's exotic 7-spheres. This book is based on courses the author taught in Mainz and Heidelberg. Readers should be familiar with the basic notions of point-set topology and differential topology. The book can be used for a combined introduction to differential and algebraic topology, as well as for a quick presentation of (co)homology in a course about differential geometry.

Author : Morris W. Hirsch
Publisher : Springer Science & Business Media
Page : 230 pages
File Size : 52,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468494495

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Differential Topology by Morris W. Hirsch Pdf

"A very valuable book. In little over 200 pages, it presents a well-organized and surprisingly comprehensive treatment of most of the basic material in differential topology, as far as is accessible without the methods of algebraic topology....There is an abundance of exercises, which supply many beautiful examples and much interesting additional information, and help the reader to become thoroughly familiar with the material of the main text." —MATHEMATICAL REVIEWS

Author : Edmond A. Jonckheere
Publisher : Oxford University Press, USA
Page : 625 pages
File Size : 42,9 Mb
Release : 1997
Category : Algebraic topology
ISBN : 9780195093018

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Algebraic and Differential Topology of Robust Stability by Edmond A. Jonckheere Pdf

In this book, two seemingly unrelated fields - algebraic topology and robust control - are brought together. The book develops algebraic/differential topology proceeding from an easily motivated control engineering problem, showing the relevance of advanced topological concepts and reconstructing the fundamental concepts of algebraic/differential topology from an application-oriented point of view. It is suitable for graduate students in engineering and/or applied mathematics, and academic researchers.

Author : M. Karoubi,C. Leruste
Publisher : Cambridge University Press
Page : 380 pages
File Size : 41,9 Mb
Release : 1987
Category : Mathematics
ISBN : 0521317142

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Algebraic Topology Via Differential Geometry by M. Karoubi,C. Leruste Pdf

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.

Author : Loring W. Tu
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 48,6 Mb
Release : 2010-10-05
Category : Mathematics
ISBN : 9781441974006

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An Introduction to Manifolds by Loring W. Tu Pdf

Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.

Author : J. P. May
Publisher : University of Chicago Press
Page : 262 pages
File Size : 53,5 Mb
Release : 1999-09
Category : Mathematics
ISBN : 0226511839

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A Concise Course in Algebraic Topology by J. P. May Pdf

Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.

Author : John Willard Milnor,David W. Weaver
Publisher : Princeton University Press
Page : 80 pages
File Size : 42,6 Mb
Release : 1997-12-14
Category : Mathematics
ISBN : 0691048339

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Topology from the Differentiable Viewpoint by John Willard Milnor,David W. Weaver Pdf

This elegant book by distinguished mathematician John Milnor, provides a clear and succinct introduction to one of the most important subjects in modern mathematics. Beginning with basic concepts such as diffeomorphisms and smooth manifolds, he goes on to examine tangent spaces, oriented manifolds, and vector fields. Key concepts such as homotopy, the index number of a map, and the Pontryagin construction are discussed. The author presents proofs of Sard's theorem and the Hopf theorem.

Author : R.V. Gamkrelidze
Publisher : Routledge
Page : 252 pages
File Size : 51,6 Mb
Release : 2022-01-27
Category : Mathematics
ISBN : 9781351467544

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Algebraic and Differential Topology by R.V. Gamkrelidze Pdf

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.

Author : Victor Guillemin,Alan Pollack
Publisher : American Mathematical Soc.
Page : 242 pages
File Size : 41,9 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821851937

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Differential Topology by Victor Guillemin,Alan Pollack Pdf

Differential Topology provides an elementary and intuitive introduction to the study of smooth manifolds. In the years since its first publication, Guillemin and Pollack's book has become a standard text on the subject. It is a jewel of mathematical exposition, judiciously picking exactly the right mixture of detail and generality to display the richness within. The text is mostly self-contained, requiring only undergraduate analysis and linear algebra. By relying on a unifying idea--transversality--the authors are able to avoid the use of big machinery or ad hoc techniques to establish the main results. In this way, they present intelligent treatments of important theorems, such as the Lefschetz fixed-point theorem, the Poincaré-Hopf index theorem, and Stokes theorem. The book has a wealth of exercises of various types. Some are routine explorations of the main material. In others, the students are guided step-by-step through proofs of fundamental results, such as the Jordan-Brouwer separation theorem. An exercise section in Chapter 4 leads the student through a construction of de Rham cohomology and a proof of its homotopy invariance. The book is suitable for either an introductory graduate course or an advanced undergraduate course.

Author : Anant R. Shastri
Publisher : CRC Press
Page : 319 pages
File Size : 46,6 Mb
Release : 2011-03-04
Category : Mathematics
ISBN : 9781439831632

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Elements of Differential Topology by Anant R. Shastri Pdf

Derived from the author's course on the subject, Elements of Differential Topology explores the vast and elegant theories in topology developed by Morse, Thom, Smale, Whitney, Milnor, and others. It begins with differential and integral calculus, leads you through the intricacies of manifold theory, and concludes with discussions on algebraic topol

Author : R. Bott,S. Gitler
Publisher : Springer
Page : 183 pages
File Size : 43,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540376163

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Lectures on Algebraic and Differential Topology by R. Bott,S. Gitler Pdf

Author : Allen Hatcher
Publisher : Cambridge University Press
Page : 572 pages
File Size : 42,7 Mb
Release : 2002
Category : Mathematics
ISBN : 0521795400

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Algebraic Topology by Allen Hatcher Pdf

An introductory textbook suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises.