Algebraic And Differential Topology
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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
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.
Lectures On Algebraic And Differential Topology
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Author : R. Bott
language : en
Publisher: Springer
Release Date : 2006-11-15
Lectures On Algebraic And Differential Topology written by R. Bott and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Algebraic And Differential Topology
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Author : R. V. Gamkrelidze
language : en
Publisher: CRC Press
Release Date : 1987-03-06
Algebraic And Differential Topology written by R. V. Gamkrelidze and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-03-06 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.
Algebraic Topology Via Differential Geometry
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Author : M. Karoubi
language : en
Publisher: Cambridge University Press
Release Date : 1987
Algebraic Topology Via Differential Geometry written by M. Karoubi and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.
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.
Differential Forms In Algebraic Topology
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Author : Raoul Bott
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Differential Forms In Algebraic Topology written by Raoul Bott 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 2013-04-17 with Mathematics categories.
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.
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
Algebraic And Differential Topology Of Robust Stability
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Author : Edmond A. Jonckheere
language : en
Publisher: Oxford University Press
Release Date : 1997-05-29
Algebraic And Differential Topology Of Robust Stability written by Edmond A. Jonckheere and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-05-29 with Mathematics categories.
In this book, two seemingly unrelated fields -- algebraic topology and robust control -- are brought together. The book develops algebraic/differential topology from an application-oriented point of view. The book takes the reader on a path starting from a well-motivated robust stability problem, showing the relevance of the simplicial approximation theorem and how it can be efficiently implemented using computational geometry. The simplicial approximation theorem serves as a primer to more serious topological issues such as the obstruction to extending the Nyquist map, K-theory of robust stabilization, and eventually the differential topology of the Nyquist map, culminating in the explanation of the lack of continuity of the stability margin relative to rounding errors. The book is suitable for graduate students in engineering and/or applied mathematics, academic researchers and governmental laboratories.
Differential Algebraic Topology
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Author : Matthias Kreck
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Differential Algebraic Topology written by Matthias Kreck and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
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.
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.