Download or read book Rational Homotopy Theory written by Yves Felix and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Rational Homotopy Theory and Differential Forms written by Phillip Griffiths and published by Springer Science & Business Media. This book was released on 2013-10-02 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Rational Homotopy Theory II written by Yves Félix and published by World Scientific. This book was released on 2015-02-11 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book On PL DeRham Theory and Rational Homotopy Type written by Aldridge Knight Bousfield and published by American Mathematical Soc.. This book was released on 1976 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Homotopy of Operads and Grothendieck Teichmuller Groups written by Benoit Fresse and published by American Mathematical Soc.. This book was released on 2017-04-21 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Grothendieck–Teichmüller group was defined by Drinfeld in quantum group theory with insights coming from the Grothendieck program in Galois theory. The ultimate goal of this book is to explain that this group has a topological interpretation as a group of homotopy automorphisms associated to the operad of little 2-discs, which is an object used to model commutative homotopy structures in topology. This volume gives a comprehensive survey on the algebraic aspects of this subject. The book explains the definition of an operad in a general context, reviews the definition of the little discs operads, and explains the definition of the Grothendieck–Teichmüller group from the viewpoint of the theory of operads. In the course of this study, the relationship between the little discs operads and the definition of universal operations associated to braided monoidal category structures is explained. Also provided is a comprehensive and self-contained survey of the applications of Hopf algebras to the definition of a rationalization process, the Malcev completion, for groups and groupoids. Most definitions are carefully reviewed in the book; it requires minimal prerequisites to be accessible to a broad readership of graduate students and researchers interested in the applications of operads.
Download or read book Local Algebra written by Jean-Pierre Serre and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an English translation of the now classic "Algbre Locale - Multiplicits" originally published by Springer as LNM 11. It gives a short account of the main theorems of commutative algebra, with emphasis on modules, homological methods and intersection multiplicities. Many modifications to the original French text have been made for this English edition, making the text easier to read, without changing its intended informal character.
Download or read book Algebraic Homotopy written by Hans J. Baues and published by Cambridge University Press. This book was released on 1989-02-16 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a general outlook on homotopy theory; fundamental concepts, such as homotopy groups and spectral sequences, are developed from a few axioms and are thus available in a broad variety of contexts. Many examples and applications in topology and algebra are discussed, including an introduction to rational homotopy theory in terms of both differential Lie algebras and De Rham algebras. The author describes powerful tools for homotopy classification problems, particularly for the classification of homotopy types and for the computation of the group homotopy equivalences. Applications and examples of such computations are given, including when the fundamental group is non-trivial. Moreover, the deep connection between the homotopy classification problems and the cohomology theory of small categories is demonstrated. The prerequisites of the book are few: elementary topology and algebra. Consequently, this account will be valuable for non-specialists and experts alike. It is an important supplement to the standard presentations of algebraic topology, homotopy theory, category theory and homological algebra.
Download or read book Elements of Homotopy Theory written by George W. Whitehead and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the title suggests, this book is concerned with the elementary portion of the subject of homotopy theory. It is assumed that the reader is familiar with the fundamental group and with singular homology theory, including the Universal Coefficient and Kiinneth Theorems. Some acquaintance with manifolds and Poincare duality is desirable, but not essential. Anyone who has taught a course in algebraic topology is familiar with the fact that a formidable amount of technical machinery must be introduced and mastered before the simplest applications can be made. This phenomenon is also observable in the more advanced parts of the subject. I have attempted to short-circuit it by making maximal use of elementary methods. This approach entails a leisurely exposition in which brevity and perhaps elegance are sacrificed in favor of concreteness and ease of application. It is my hope that this approach will make homotopy theory accessible to workers in a wide range of other subjects-subjects in which its impact is beginning to be felt. It is a consequence of this approach that the order of development is to a certain extent historical. Indeed, if the order in which the results presented here does not strictly correspond to that in which they were discovered, it nevertheless does correspond to an order in which they might have been discovered had those of us who were working in the area been a little more perspicacious.
Download or read book Rational Homotopy Theory Draft Version 96 2 written by Steve Halperin and published by . This book was released on 1996 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Homotopy Type Theory Univalent Foundations of Mathematics written by and published by Univalent Foundations. This book was released on with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nilpotence and Periodicity in Stable Homotopy Theory written by Douglas C. Ravenel and published by Princeton University Press. This book was released on 1992-11-08 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nilpotence and Periodicity in Stable Homotopy Theory describes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which were conjectured by the author in 1977 and proved by Devinatz, Hopkins, and Smith in 1985. During the last ten years a number of significant advances have been made in homotopy theory, and this book fills a real need for an up-to-date text on that topic. Ravenel's first few chapters are written with a general mathematical audience in mind. They survey both the ideas that lead up to the theorems and their applications to homotopy theory. The book begins with some elementary concepts of homotopy theory that are needed to state the problem. This includes such notions as homotopy, homotopy equivalence, CW-complex, and suspension. Next the machinery of complex cobordism, Morava K-theory, and formal group laws in characteristic p are introduced. The latter portion of the book provides specialists with a coherent and rigorous account of the proofs. It includes hitherto unpublished material on the smash product and chromatic convergence theorems and on modular representations of the symmetric group.
Download or read book Rational Homotopy Type written by Wen-tsün Wu and published by Springer. This book was released on 2006-11-14 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Rational Homotopy Theory written by Yves Felix and published by . This book was released on 2011-04-26 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lie Models in Topology written by Urtzi Buijs and published by Springer Nature. This book was released on 2020-12-15 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the birth of rational homotopy theory, the possibility of extending the Quillen approach – in terms of Lie algebras – to a more general category of spaces, including the non-simply connected case, has been a challenge for the algebraic topologist community. Despite the clear Eckmann-Hilton duality between Quillen and Sullivan treatments, the simplicity in the realization of algebraic structures in the latter contrasts with the complexity required by the Lie algebra version. In this book, the authors develop new tools to address these problems. Working with complete Lie algebras, they construct, in a combinatorial way, a cosimplicial Lie model for the standard simplices. This is a key object, which allows the definition of a new model and realization functors that turn out to be homotopically equivalent to the classical Quillen functors in the simply connected case. With this, the authors open new avenues for solving old problems and posing new questions. This monograph is the winner of the 2020 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics.
Download or read book Equivariant Homotopy and Cohomology Theory written by J. Peter May and published by American Mathematical Soc.. This book was released on 1996 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume introduces equivariant homotopy, homology, and cohomology theory, along with various related topics in modern algebraic topology. It explains the main ideas behind some of the most striking recent advances in the subject. The works begins with a development of the equivariant algebraic topology of spaces culminating in a discussion of the Sullivan conjecture that emphasizes its relationship with classical Smith theory. The book then introduces equivariant stable homotopy theory, the equivariant stable homotopy category, and the most important examples of equivariant cohomology theories. The basic machinery that is needed to make serious use of equivariant stable homotopy theory is presented next, along with discussions of the Segal conjecture and generalized Tate cohomology. Finally, the book gives an introduction to "brave new algebra", the study of point-set level algebraic structures on spectra and its equivariant applications. Emphasis is placed on equivariant complex cobordism, and related results on that topic are presented in detail.
Download or read book From Categories to Homotopy Theory written by Birgit Richter and published by Cambridge University Press. This book was released on 2020-04-16 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Category theory provides structure for the mathematical world and is seen everywhere in modern mathematics. With this book, the author bridges the gap between pure category theory and its numerous applications in homotopy theory, providing the necessary background information to make the subject accessible to graduate students or researchers with a background in algebraic topology and algebra. The reader is first introduced to category theory, starting with basic definitions and concepts before progressing to more advanced themes. Concrete examples and exercises illustrate the topics, ranging from colimits to constructions such as the Day convolution product. Part II covers important applications of category theory, giving a thorough introduction to simplicial objects including an account of quasi-categories and Segal sets. Diagram categories play a central role throughout the book, giving rise to models of iterated loop spaces, and feature prominently in functor homology and homology of small categories.
Download or read book Cohomological Methods in Transformation Groups written by C. Allday and published by Cambridge University Press. This book was released on 1993-07 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an account of the theory of certain types of compact transformation groups, namely those that are susceptible to study using ordinary cohomology theory and rational homotopy theory, which in practice means the torus groups and elementary abelian p-groups. The efforts of many mathematicians have combined to bring a depth of understanding to this area. However to make it reasonably accessible to a wide audience, the authors have streamlined the presentation, referring the reader to the literature for purely technical results and working in a simplified setting where possible. In this way the reader with a relatively modest background in algebraic topology and homology theory can penetrate rather deeply into the subject, whilst the book at the same time makes a useful reference for the more specialised reader.
