On Pl De Rham Theory And Rational Homotopy Type
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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.
The rational [bold]PL de Rham theory of Sullivan is developed and generalized, using methods of Quillen's "homotopical algebra." For a field k of characteristic 0, a pair of contravariant adjoint functors A : (Simplicial sets) [right arrow over left arrow] (Commutative DG k-algebras) : F is obtained which pass to the appropriate homotopy categories. When k is the field of rationals, these functors induce equivalence between the appropriate simplicial and algebraic rational homotopy categories. The theory is not restricted to simply connected spaces. It is closely related to the theory of "rational localization" (for nilpotent spaces) and "rational completion" in general.
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.
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 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.
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
Topology And Its Applications
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Author : Sergeĭ Petrovich Novikov
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Topology And Its Applications written by Sergeĭ Petrovich Novikov 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 1993 with Mathematics categories.
The Proceedings of an international topology conference - this book covrs various aspects of general algebraic, and low-dimensional topology.
Homotopy Theory Of Function Spaces And Related Topics
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Author : Yves Félix
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Homotopy Theory Of Function Spaces And Related Topics written by Yves Félix 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 volume contains the proceedings of the Workshop on Homotopy Theory of Function Spaces and Related Topics, which was held at the Mathematisches Forschungsinstitut Oberwolfach, in Germany, from April 5-11, 2009. This volume contains fourteen original research articles covering a broad range of topics that include: localization and rational homotopy theory, evaluation subgroups, free loop spaces, Whitehead products, spaces of algebraic maps, gauge groups, loop groups, operads, and string topology. In addition to reporting on various topics in the area, this volume is supposed to facilitate the exchange of ideas within Homotopy Theory of Function Spaces, and promote cross-fertilization between Homotopy Theory of Function Spaces and other areas. With these latter aims in mind, this volume includes a survey article which, with its extensive bibliography, should help bring researchers and graduate students up to speed on activity in this field as well as a problems list, which is an expanded and edited version of problems discussed in sessions held at the conference. The problems list is intended to suggest directions for future work.
Rational Homotopical Models And Uniqueness
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Author : Martin Majewski
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Rational Homotopical Models And Uniqueness written by Martin Majewski 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 2000 with Mathematics categories.
The main goal of this paper is to prove the following conjecture of Baues and Lemaire: the differential graded Lie Tlgebra associated with the Sullivan model of a space is homotopy equivalent to its Quillen model. In addition we show the same for the cellular Lie algebra model which we build from the simplicial analog of the classical Adams-Hilton model. It turns out that this cellular Lie algebra model is one link in a chain of models connecting the models of Quillen and Sullivan.The key result which makes all this possible is Anick's correspondence between differential graded Lie algebras and Hopf algebras up to homotopy. In addition we show that the Quillen model is a rational homotopical equivalence, and we conclude the same for the other models using our main result. Theconstruction of the three models is given in detail. The background from homotopy theory, differential algebra, and algebra is presented in great generality.