Rational Homotopy Theory PDF Download
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Author | : Yves Felix |
Publisher | : Springer Science & Business Media |
Total Pages | : 574 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 146130105X |
Download Rational Homotopy Theory Book in PDF, ePub and Kindle
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.
Author | : Phillip Griffiths |
Publisher | : Springer Science & Business Media |
Total Pages | : 228 |
Release | : 2013-10-02 |
Genre | : Mathematics |
ISBN | : 1461484685 |
Download Rational Homotopy Theory and Differential Forms Book in PDF, ePub and Kindle
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.
Author | : Steve Halperin |
Publisher | : World Scientific |
Total Pages | : 449 |
Release | : 2015-02-11 |
Genre | : Mathematics |
ISBN | : 9814651451 |
Download Rational Homotopy Theory Ii Book in PDF, ePub and Kindle
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.
Author | : Wen-tsün Wu |
Publisher | : Springer |
Total Pages | : 228 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540390251 |
Download Rational Homotopy Type Book in PDF, ePub and Kindle
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.
Author | : Aldridge Knight Bousfield |
Publisher | : American Mathematical Soc. |
Total Pages | : 108 |
Release | : 1976 |
Genre | : Mathematics |
ISBN | : 0821821792 |
Download On PL DeRham Theory and Rational Homotopy Type Book in PDF, ePub and Kindle
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.
Author | : Steve Halperin |
Publisher | : |
Total Pages | : 199 |
Release | : 1996 |
Genre | : |
ISBN | : |
Download Rational Homotopy Theory (Draft, Version 96.2) Book in PDF, ePub and Kindle
Author | : Yves Felix |
Publisher | : |
Total Pages | : 588 |
Release | : 2011-04-26 |
Genre | : |
ISBN | : 9781461301066 |
Download Rational Homotopy Theory Book in PDF, ePub and Kindle
Author | : Jean-Pierre Serre |
Publisher | : Springer Science & Business Media |
Total Pages | : 139 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3662042037 |
Download Local Algebra Book in PDF, ePub and Kindle
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.
Author | : Yves Felix |
Publisher | : Springer |
Total Pages | : 252 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540392041 |
Download Algebraic Topology - Rational Homotopy Book in PDF, ePub and Kindle
This proceedings volume centers on new developments in rational homotopy and on their influence on algebra and algebraic topology. Most of the papers are original research papers dealing with rational homotopy and tame homotopy, cyclic homology, Moore conjectures on the exponents of the homotopy groups of a finite CW-c-complex and homology of loop spaces. Of particular interest for specialists are papers on construction of the minimal model in tame theory and computation of the Lusternik-Schnirelmann category by means articles on Moore conjectures, on tame homotopy and on the properties of Poincaré series of loop spaces.
Author | : George W. Whitehead |
Publisher | : Springer Science & Business Media |
Total Pages | : 764 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461263182 |
Download Elements of Homotopy Theory Book in PDF, ePub and Kindle
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.