Homotopy Theoretic Methods In Group Cohomology
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Homotopy Theoretic Methods In Group Cohomology
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Author : William G. Dwyer
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Homotopy Theoretic Methods In Group Cohomology written by William G. Dwyer and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book consists essentially of notes which were written for an Advanced Course on Classifying Spaces and Cohomology of Groups. The course took place at the Centre de Recerca Mathematica (CRM) in Bellaterra from May 27 to June 2, 1998 and was part of an emphasis semester on Algebraic Topology. It consisted of two parallel series of 6 lectures of 90 minutes each and was intended as an introduction to new homotopy theoretic methods in group cohomology. The first part of the book is concerned with methods of decomposing the classifying space of a finite group into pieces made of classifying spaces of appropriate subgroups. Such decompositions have been used with great success in the last 10-15 years in the homotopy theory of classifying spaces of compact Lie groups and p-compact groups in the sense of Dwyer and Wilkerson. For simplicity the emphasis here is on finite groups and on homological properties of various decompositions known as centralizer resp. normalizer resp. subgroup decomposition. A unified treatment of the various decompositions is given and the relations between them are explored. This is preceeded by a detailed discussion of basic notions such as classifying spaces, simplicial complexes and homotopy colimits.
Homotopy Theory And Its Applications
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Author : Alejandro Adem
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Homotopy Theory And Its Applications written by Alejandro Adem and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Homotopy theory categories.
This book is the result of a conference held to examine developments in homotopy theory in honor of Samuel Gitler in July 1993 (Cocoyoc, Mexico). It includes several research papers and three expository papers on various topics in homotopy theory. The research papers discuss the following: BL application of homotopy theory to group theory BL fiber bundle theory BL homotopy theory The expository papers consider the following topics: BL the Atiyah-Jones conjecture (by C. Boyer) BL classifying spaces of finite groups (by J. Martino) BL instanton moduli spaces (by J. Milgram) Homotopy Theory and Its Applications offers a distinctive account of how homotopy theoretic methods can be applied to a variety of interesting problems.
Homotopy Methods In Algebraic Topology
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Author : Nicholas Kuhn
language : en
Publisher: American Mathematical Soc.
Release Date : 2001-04-25
Homotopy Methods In Algebraic Topology written by Nicholas Kuhn and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-04-25 with Algebraic topology categories.
This volume presents the proceedings from the AMS-IMS-SIAM Summer Research Conference on Homotopy Methods in Algebraic Topology held at the University of Colorado (Boulder). The conference coincided with the sixtieth birthday of J. Peter May. An article is included reflecting his wide-ranging and influential contributions to the subject area. Other articles in the book discuss the ordinary, elliptic and real-oriented Adams spectral sequences, mapping class groups, configuration spaces, extended powers, operads, the telescope conjecture, $p$-compact groups, algebraic K theory, stable and unstable splittings, the calculus of functors, the $E_{\infty}$ tensor product, and equivariant cohomology theories. The book offers a compendious source on modern aspects of homotopy theoretic methods in many algebraic settings.
Cohomology Of Finite Groups
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Author : Alejandro Adem
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Cohomology Of Finite Groups written by Alejandro Adem and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
The cohomology of groups has, since its beginnings in the 1920s and 1930s, been the stage for significant interaction between algebra and topology and has led to the creation of important new fields in mathematics, like homological algebra and algebraic K-theory. This is the first book to deal comprehensively with the cohomology of finite groups: it introduces the most important and useful algebraic and topological techniques, and describes the interplay of the subject with those of homotopy theory, representation theory and group actions. The combination of theory and examples, together with the techniques for computing the cohomology of important classes of groups including symmetric groups, alternating groups, finite groups of Lie type, and some of the sporadic simple groups, enable readers to acquire an in-depth understanding of group cohomology and its extensive applications.
Cohomology Operations And Applications In Homotopy Theory
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Author : Robert E. Mosher
language : en
Publisher: Courier Corporation
Release Date : 2008-01-01
Cohomology Operations And Applications In Homotopy Theory written by Robert E. Mosher and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.
Cohomology operations are at the center of a major area of activity in algebraic topology. This treatment explores the single most important variety of operations, the Steenrod squares. It constructs these operations, proves their major properties, and provides numerous applications, including several different techniques of homotopy theory useful for computation. 1968 edition.
Cohomological Methods In Homotopy Theory
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Author : Jaume Aguade
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Cohomological Methods In Homotopy Theory written by Jaume Aguade and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book contains a collection of articles summarizing the state of knowledge in a large portion of modern homotopy theory. A call for articles was made on the occasion of an emphasis semester organized by the Centre de Recerca Matemtica in Bellaterra (Barcelona) in 1998. The main topics treated in the book include abstract features of stable and unstable homotopy, homotopical localizations, p-compact groups, H-spaces, classifying spaces for proper actions, cohomology of discrete groups, K-theory and other generalized cohomology theories, configuration spaces, and Lusternik-Schnirelmann category. The book is addressed to all mathematicians interested in homotopy theory and in geometric aspects of group theory. New research directions in topology are highlighted. Moreover, this informative and educational book serves as a welcome reference for many new results and recent methods.
Cohomological Methods In Transformation Groups
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Author : C. Allday
language : en
Publisher: Cambridge University Press
Release Date : 1993-07
Cohomological Methods In Transformation Groups written by C. Allday and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-07 with Mathematics categories.
This is an account of the theory of certain types of compact transformation groups, namely those that are susceptible to study using ordinary cohomology theory and rational homotopy theory, which in practice means the torus groups and elementary abelian p-groups. The efforts of many mathematicians have combined to bring a depth of understanding to this area. However to make it reasonably accessible to a wide audience, the authors have streamlined the presentation, referring the reader to the literature for purely technical results and working in a simplified setting where possible. In this way the reader with a relatively modest background in algebraic topology and homology theory can penetrate rather deeply into the subject, whilst the book at the same time makes a useful reference for the more specialised reader.
Algebraic Methods In Unstable Homotopy Theory
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Author : Joseph Neisendorfer
language : en
Publisher: Cambridge University Press
Release Date : 2010-02-18
Algebraic Methods In Unstable Homotopy Theory written by Joseph Neisendorfer and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-02-18 with Mathematics categories.
The most modern and thorough treatment of unstable homotopy theory available. The focus is on those methods from algebraic topology which are needed in the presentation of results, proven by Cohen, Moore, and the author, on the exponents of homotopy groups. The author introduces various aspects of unstable homotopy theory, including: homotopy groups with coefficients; localization and completion; the Hopf invariants of Hilton, James, and Toda; Samelson products; homotopy Bockstein spectral sequences; graded Lie algebras; differential homological algebra; and the exponent theorems concerning the homotopy groups of spheres and Moore spaces. This book is suitable for a course in unstable homotopy theory, following a first course in homotopy theory. It is also a valuable reference for both experts and graduate students wishing to enter the field.
Topological Methods In Group Theory
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Author : Ross Geoghegan
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-27
Topological Methods In Group Theory written by Ross Geoghegan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-27 with Mathematics categories.
This book is about the interplay between algebraic topology and the theory of infinite discrete groups. It is a hugely important contribution to the field of topological and geometric group theory, and is bound to become a standard reference in the field. To keep the length reasonable and the focus clear, the author assumes the reader knows or can easily learn the necessary algebra, but wants to see the topology done in detail. The central subject of the book is the theory of ends. Here the author adopts a new algebraic approach which is geometric in spirit.
Diagram Cohomology And Isovariant Homotopy Theory
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Author : Giora Dula
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Diagram Cohomology And Isovariant Homotopy Theory written by Giora Dula and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
In algebraic topology, obstruction theory provides a way to study homotopy classes of continuous maps in terms of cohomology groups; a similar theory exists for certain spaces with group actions and maps that are compatible (that is, equivariant) with respect to the group actions. This work provides a corresponding setting for certain spaces with group actions and maps that are compatible in a stronger sense, called isovariant. The basic idea is to establish an equivalence between isovariant homotopy and equivariant homotopy for certain categories of diagrams. Consequences include isovariant versions of the usual Whitehead theorems for recognizing homotopy equivalences, an obstruction theory for deforming equivariant maps to isovariant maps, rational computations for the homotopy groups of certain spaces of isovariant functions, and applications to constructions and classification problems for differentiable group actions.