rational homotopy theory and differential forms 16 progress in mathematics

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Rational Homotopy Theory And Differential Forms

Author : Phillip Griffiths
ISBN : 9781461484684
Genre : Mathematics
File Size : 65. 64 MB
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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 Theory

Author : Yves Felix
ISBN : 9781461301059
Genre : Mathematics
File Size : 43. 11 MB
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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 Type

Author : Wen-tsün Wu
ISBN : 9783540390251
Genre : Mathematics
File Size : 49. 32 MB
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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.

Rational Homotopical Models And Uniqueness

Author : Martin Majewski
ISBN : 9780821819203
Genre : Mathematics
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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 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. The construction of the three models is given in detail. The background from homotopy theory, differential algebra, and algebra is presented in great generality.

Homotopy Theory And Related Topics

Author : Hiroshi Toda
ISBN : UCAL:B4406927
Genre : Mathematics
File Size : 38. 25 MB
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Annales Scientifiques De L Cole Normale Sup Rieure

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ISBN : UOM:39015059010994
Genre : Science
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Bolet N De La Sociedad Matem Tica Mexicana

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ISBN : CORNELL:31924089803401
Genre : Mathematics
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Pamq

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ISBN : UOM:39015072604062
Genre : Mathematics
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Reviews In Global Analysis 1980 86 As Printed In Mathematical Reviews

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ISBN : UCAL:B4342570
Genre : Mathematics
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Revue Roumaine De Math Matiques Pures Et Applique S

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ISBN : UOM:39015049362083
Genre : Mathematics
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