Rational Homotopical Models And 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 | : 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 | : |
| Publisher | : |
| Total Pages | : 224 |
| Release | : 1992-12 |
| Genre | : |
| ISBN | : |
Download Canadian Journal of Mathematics Book in PDF, ePub and Kindle
| Author | : Serge Bouc |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 89 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 0821819518 |
Download Non-Additive Exact Functors and Tensor Induction for Mackey Functors Book in PDF, ePub and Kindle
First the author introduces a generalization of the notion of (right)-exact functor between abelian categories to the case of non-additive functors. The main result of this section is an extension theorem: any functor defined on a suitable subcategory can be extended uniquely to a right exact functor defined on the whole category. Next those results are used to define various functors of generalized tensor induction, associated to finite bisets, between categories attached to finite groups. This includes a definition of tensor induction for Mackey functors, for cohomological Mackey functors, for p-permutation modules and algebras. This also gives a single formalism of bisets for restriction, inflation, and ordinary tensor induction for modules.
| Author | : Jean-Luc Joly |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 87 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 0821820419 |
Download Caustics for Dissipative Semilinear Oscillations Book in PDF, ePub and Kindle
This book is intended for graduate students and research mathematicians interested in partial differential equations.
| Author | : Harvey I. Blau |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 109 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 0821820214 |
Download Homogeneous Integral Table Algebras of Degree Three: A Trilogy Book in PDF, ePub and Kindle
Homogeneous integral table algebras of degree three with a faithful real element. The algebras of the title are classified to exact isomorphism; that is, the sets of structure constants which arise from the given basis are completely determined. Other results describe all possible extensions (pre-images), with a faithful element which is not necessarily real, of certain simple homogeneous integral table algebras of degree three. On antisymmetric homogeneous integral table algebras of degree three. This paper determines the homogeneous integral table algebras of degree three in which the given basis has a faithful element and has no nontrivial elements that are either real (symmetric) or linear, and where an additional hypothesis is satisfied. It is shown that all such bases must occur as the set of orbit sums in the complex group algebra of a finite abelian group under the action of a fixed-point-free automorphism oforder three. Homogeneous integral table algebras of degree three with no nontrivial linear elements. The algebras of the title which also have a faithful element are determined to exact isomorphism. All of the simple homogeneous integral table algebras of degree three are displayed, and the commutative association schemes in which all the nondiagonal relations have valency three and where some relation defines a connected graph on the underlying set are classified up to algebraic isomorphism.
