Rational Homotopy Theory And Differential Forms
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Rational Homotopy Theory And Differential Forms
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Author : Phillip Griffiths
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-02
Rational Homotopy Theory And Differential Forms written by Phillip Griffiths 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 2013-10-02 with Mathematics categories.
This completely revised and corrected version of the well-known Florence notes circulated by the authors together with E. Friedlander examines basic topology, emphasizing homotopy theory. Included is a discussion of Postnikov towers and rational homotopy theory. This is then followed by an in-depth look at differential forms and de Tham’s theorem on simplicial complexes. In addition, Sullivan’s results on computing the rational homotopy type from forms is presented. New to the Second Edition: *Fully-revised appendices including an expanded discussion of the Hirsch lemma *Presentation of a natural proof of a Serre spectral sequence result *Updated content throughout the book, reflecting advances in the area of homotopy theory With its modern approach and timely revisions, this second edition of Rational Homotopy Theory and Differential Forms will be a valuable resource for graduate students and researchers in algebraic topology, differential forms, and homotopy theory.
Rational Homotopy Theory And Differential Forms
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Author : Phillip A. Griffiths
language : en
Publisher: Springer
Release Date : 1981
Rational Homotopy Theory And Differential Forms written by Phillip A. Griffiths and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
Rational Homotopy Type
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Author : Wen-tsün Wu
language : en
Publisher: Springer
Release Date : 2006-11-14
Rational Homotopy Type written by Wen-tsün Wu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
This comprehensive monograph provides a self-contained treatment of the theory of I*-measure, or Sullivan's rational homotopy theory, from a constructive point of view. It centers on the notion of calculability which is due to the author himself, as are the measure-theoretical and constructive points of view in rational homotopy. The I*-measure is shown to differ from other homology and homotopy measures in that it is calculable with respect to most of the important geometric constructions encountered in algebraic topology. This approach provides a new method of treatment and leads to various new results. In particular, an axiomatic system of I*-measure is formulated, quite different in spirit from the usual Eilenberg-Steenrod axiomatic system for homology, and giving at the same time an algorithmic method of computation of the I*-measure in concrete cases. The book will be of interest to researchers in rational homotopy theory and will provide them with new ideas and lines of research to develop further.
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.
On Pl Derham Theory And Rational Homotopy Type
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Author : Aldridge Knight Bousfield
language : en
Publisher: American Mathematical Soc.
Release Date : 1976
On Pl Derham Theory And Rational Homotopy Type written by Aldridge Knight Bousfield 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 1976 with Mathematics categories.
Rational Homotopy Type
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Author : Wen-tsun Wu
language : en
Publisher:
Release Date : 2014-01-15
Rational Homotopy Type written by Wen-tsun Wu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
On Pl De Rham Theory And Rational Homotopy Type
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Author : Aldridge Knight Bousfield
language : en
Publisher:
Release Date : 1976
On Pl De Rham Theory And Rational Homotopy Type written by Aldridge Knight Bousfield and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Algebra, Homological categories.
Character Map In Non Abelian Cohomology The Twisted Differential And Generalized
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Author : Domenico Fiorenza
language : en
Publisher: World Scientific
Release Date : 2023-08-11
Character Map In Non Abelian Cohomology The Twisted Differential And Generalized written by Domenico Fiorenza and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-11 with Mathematics categories.
This book presents a novel development of fundamental and fascinating aspects of algebraic topology and mathematical physics: 'extra-ordinary' and further generalized cohomology theories enhanced to 'twisted' and differential-geometric form, with focus on, firstly, their rational approximation by generalized Chern character maps, and then, the resulting charge quantization laws in higher n-form gauge field theories appearing in string theory and the classification of topological quantum materials.Although crucial for understanding famously elusive effects in strongly interacting physics, the relevant higher non-abelian cohomology theory ('higher gerbes') has had an esoteric reputation and remains underdeveloped.Devoted to this end, this book's theme is that various generalized cohomology theories are best viewed through their classifying spaces (or moduli stacks) — not necessarily infinite-loop spaces — from which perspective the character map is really an incarnation of the fundamental theorem of rational homotopy theory, thereby not only uniformly subsuming the classical Chern character and a multitude of scattered variants that have been proposed, but now seamlessly applicable in the hitherto elusive generality of (twisted, differential, and) non-abelian cohomology.In laying out this result with plenty of examples, this book provides a modernized introduction and review of fundamental classical topics: 1. abstract homotopy theory via model categories; 2. generalized cohomology in its homotopical incarnation; 3. rational homotopy theory seen via homotopy Lie theory, whose fundamental theorem we recast as a (twisted) non-abelian de Rham theorem, which naturally induces the (twisted) non-abelian character map.
Rational Homotopy Theory
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Author : Yves Felix
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Rational Homotopy Theory written by Yves Felix 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 2012-12-06 with Mathematics categories.
Rational homotopy theory is a subfield of algebraic topology. Written by three authorities in the field, this book contains all the main theorems of the field with complete proofs. As both notation and techniques of rational homotopy theory have been considerably simplified, the book presents modern elementary proofs for many results that were proven ten or fifteen years ago.
Rational Homotopy Theory Ii
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Author : Yves Félix
language : en
Publisher: World Scientific
Release Date : 2015-02-11
Rational Homotopy Theory Ii written by Yves Félix and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-11 with Mathematics categories.
This research monograph is a detailed account with complete proofs of rational homotopy theory for general non-simply connected spaces, based on the minimal models introduced by Sullivan in his original seminal article. Much of the content consists of new results, including generalizations of known results in the simply connected case. The monograph also includes an expanded version of recently published results about the growth and structure of the rational homotopy groups of finite dimensional CW complexes, and concludes with a number of open questions. This monograph is a sequel to the book Rational Homotopy Theory [RHT], published by Springer in 2001, but is self-contained except only that some results from [RHT] are simply quoted without proof. Contents:Basic Definitions and ConstructionsHomotopy Lie Algebras and Sullivan Lie AlgebrasFibrations and Λ-ExtensionsHolonomyThe Model of the Fibre is the Fibre of the ModelLoop Spaces and Loop Space ActionsSullivan SpacesExamplesLusternik-Schnirelmann CategoryDepth of a Sullivan Algebra and of a Sullivan Lie AlgebraDepth of a Connected Graded Lie Algebra of Finite TypeTrichotomyExponential GrowthStructure of a Graded Lie Algebra of Finite DepthWeight Decompositions of a Sullivan Lie AlgebraProblems Readership: Researchers in algebraic topology and Lie algebra theory.Key Features:Contains the basis for using rational homotopy theory for non-simply connected spacesContains new important information on the rational homotopy Lie algebra of spacesIs at the frontier of the research in rational homotopyKeywords:Rational Homotopy Theory;Algebraic Topology;Malcev Completion;Graded Lie Algebra