Rational Homotopy Theory Ii

Rational Homotopy Theory Ii
Author :
Publisher : World Scientific
Total Pages : 449
Release :
ISBN-10 : 9789814651455
ISBN-13 : 9814651451
Rating : 4/5 (55 Downloads)

Synopsis Rational Homotopy Theory Ii by : Steve Halperin

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.

Rational Homotopy Theory

Rational Homotopy Theory
Author :
Publisher : Springer Science & Business Media
Total Pages : 589
Release :
ISBN-10 : 9780387950686
ISBN-13 : 0387950680
Rating : 4/5 (86 Downloads)

Synopsis Rational Homotopy Theory by : Yves Felix

This is a long awaited book on rational homotopy theory which contains all the main theorems with complete proofs, and more elementary proofs for many results that were proved ten or fifteen years ago. The authors added a frist section on classical algebraic topology to make the book accessible to students with only little background in algebraic topology.

Rational Homotopy Theory and Differential Forms

Rational Homotopy Theory and Differential Forms
Author :
Publisher : Springer Science & Business Media
Total Pages : 228
Release :
ISBN-10 : 9781461484684
ISBN-13 : 1461484685
Rating : 4/5 (84 Downloads)

Synopsis Rational Homotopy Theory and Differential Forms by : Phillip Griffiths

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.

On PL DeRham Theory and Rational Homotopy Type

On PL DeRham Theory and Rational Homotopy Type
Author :
Publisher : American Mathematical Soc.
Total Pages : 108
Release :
ISBN-10 : 9780821821794
ISBN-13 : 0821821792
Rating : 4/5 (94 Downloads)

Synopsis On PL DeRham Theory and Rational Homotopy Type by : Aldridge Knight Bousfield

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.

Rational Homotopy Theory

Rational Homotopy Theory
Author :
Publisher : Springer Science & Business Media
Total Pages : 574
Release :
ISBN-10 : 9781461301059
ISBN-13 : 146130105X
Rating : 4/5 (59 Downloads)

Synopsis Rational Homotopy Theory by : Yves Felix

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.

Homotopy of Operads and Grothendieck-Teichmuller Groups

Homotopy of Operads and Grothendieck-Teichmuller Groups
Author :
Publisher : American Mathematical Soc.
Total Pages : 581
Release :
ISBN-10 : 9781470434816
ISBN-13 : 1470434814
Rating : 4/5 (16 Downloads)

Synopsis Homotopy of Operads and Grothendieck-Teichmuller Groups by : Benoit Fresse

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.

Local Algebra

Local Algebra
Author :
Publisher : Springer Science & Business Media
Total Pages : 139
Release :
ISBN-10 : 9783662042038
ISBN-13 : 3662042037
Rating : 4/5 (38 Downloads)

Synopsis Local Algebra by : Jean-Pierre Serre

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.

Algebraic Models in Geometry

Algebraic Models in Geometry
Author :
Publisher : Oxford University Press
Total Pages : 483
Release :
ISBN-10 : 9780199206513
ISBN-13 : 0199206511
Rating : 4/5 (13 Downloads)

Synopsis Algebraic Models in Geometry by : Yves Félix

A text aimed at both geometers needing the tools of rational homotopy theory to understand and discover new results concerning various geometric subjects, and topologists who require greater breadth of knowledge about geometric applications of the algebra of homotopy theory.

Equivariant Homotopy and Cohomology Theory

Equivariant Homotopy and Cohomology Theory
Author :
Publisher : American Mathematical Soc.
Total Pages : 384
Release :
ISBN-10 : 9780821803196
ISBN-13 : 0821803190
Rating : 4/5 (96 Downloads)

Synopsis Equivariant Homotopy and Cohomology Theory by : J. Peter May

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.