Rational Homotopical Models Uniqueness PDF Download
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| Author | : Martin Majewski |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 175 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 0821819208 |
Download Rational Homotopical Models and Uniqueness Book in PDF, ePub and Kindle
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.
| Author | : Martin Majewski |
| Publisher | : |
| Total Pages | : 175 |
| Release | : 2014-09-11 |
| Genre | : Homotopy theory |
| ISBN | : 9781470402730 |
Download Rational Homotopical Models & Uniqueness Book in PDF, ePub and Kindle
The main goal of this paper is to prove the following conjecture of Baues and Lemaire: the differential graded Lie algebra associated with the Sullivan model of a space is homotopy equivalent to its Quillen model. In addition, the authors show the same for the cellular Lie algebra model which they build from the simplicial analogue 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.
| 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 | : Henar Herrero |
| Publisher | : Springer Nature |
| Total Pages | : 159 |
| Release | : |
| Genre | : |
| ISBN | : 3031620259 |
Download Cutting-Edge Mathematics Book in PDF, ePub and Kindle
| Author | : Urtzi Buijs |
| Publisher | : Springer Nature |
| Total Pages | : 283 |
| Release | : 2020-12-15 |
| Genre | : Mathematics |
| ISBN | : 3030544303 |
Download Lie Models in Topology Book in PDF, ePub and Kindle
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.
| 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 | : 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 | : David Chataur |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 108 |
| Release | : 2018-08-09 |
| Genre | : |
| ISBN | : 1470428873 |
Download Intersection Cohomology, Simplicial Blow-Up and Rational Homotopy Book in PDF, ePub and Kindle
Let X be a pseudomanifold. In this text, the authors use a simplicial blow-up to define a cochain complex whose cohomology with coefficients in a field, is isomorphic to the intersection cohomology of X, introduced by M. Goresky and R. MacPherson. The authors do it simplicially in the setting of a filtered version of face sets, also called simplicial sets without degeneracies, in the sense of C. P. Rourke and B. J. Sanderson. They define perverse local systems over filtered face sets and intersection cohomology with coefficients in a perverse local system. In particular, as announced above when X is a pseudomanifold, the authors get a perverse local system of cochains quasi-isomorphic to the intersection cochains of Goresky and MacPherson, over a field. We show also that these two complexes of cochains are quasi-isomorphic to a filtered version of Sullivan's differential forms over the field Q. In a second step, they use these forms to extend Sullivan's presentation of rational homotopy type to intersection cohomology.
| Author | : Benoit Fresse |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 743 |
| Release | : 2017-05-22 |
| Genre | : Mathematics |
| ISBN | : 1470434822 |
Download Homotopy of Operads and Grothendieck-Teichmuller Groups Book in PDF, ePub and Kindle
The ultimate goal of this book is to explain that the Grothendieck–Teichmüller group, as defined by Drinfeld in quantum group theory, has a topological interpretation as a group of homotopy automorphisms associated to the little 2-disc operad. To establish this result, the applications of methods of algebraic topology to operads must be developed. This volume is devoted primarily to this subject, with the main objective of developing a rational homotopy theory for operads. The book starts with a comprehensive review of the general theory of model categories and of general methods of homotopy theory. The definition of the Sullivan model for the rational homotopy of spaces is revisited, and the definition of models for the rational homotopy of operads is then explained. The applications of spectral sequence methods to compute homotopy automorphism spaces associated to operads are also explained. This approach is used to get a topological interpretation of the Grothendieck–Teichmüller group in the case of the little 2-disc operad. This volume is intended for graduate students and researchers interested in the applications of homotopy theory methods in operad theory. It is accessible to readers with a minimal background in classical algebraic topology and operad theory.
