Cohomological Methods In Group Theory


Cohomological Methods In Group Theory
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Cohomological Methods In Group Theory


Cohomological Methods In Group Theory
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Author : Ari Babakhanian
language : en
Publisher:
Release Date : 1972

Cohomological Methods In Group Theory written by Ari Babakhanian and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Algebra, Homological categories.




Cohomological Methods In Group Theory


Cohomological Methods In Group Theory
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Author : Ararat Babakhanian
language : en
Publisher:
Release Date : 1972

Cohomological Methods In Group Theory written by Ararat Babakhanian and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Mathematics categories.


This book is intended for students interested in learning the use of cohomology and homology theory in solving problems in group theory. Although cohomology groups of a groups were formally defined in the early 1940s, these groups in low dimensions had been studied earlier as part of the general body of theory of groups. In the last three decades cohomology of groups has played a central role in various branches of mathematics. This book provides readers with the basic tools in cohomology of groups and to illustrate their use in obtaining group theoretic results.



Geometric And Cohomological Methods In Group Theory


Geometric And Cohomological Methods In Group Theory
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Author : Martin R. Bridson
language : en
Publisher: Cambridge University Press
Release Date : 2009-10-29

Geometric And Cohomological Methods In Group Theory written by Martin R. Bridson 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 2009-10-29 with Mathematics categories.


An extended tour through a selection of the most important trends in modern geometric group theory.



Geometric And Cohomological Methods In Group Theory


Geometric And Cohomological Methods In Group Theory
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Author : Martin R. Bridson
language : en
Publisher:
Release Date : 2014-05-14

Geometric And Cohomological Methods In Group Theory written by Martin R. Bridson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with Geometric group theory categories.


An extended tour through a selection of the most important trends in modern geometric group theory.



Cohomological Methods In Transformation Groups


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.



Cohomological Topics In Group Theory


Cohomological Topics In Group Theory
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Author : K. W. Gruenberg
language : en
Publisher: Springer
Release Date : 2006-11-15

Cohomological Topics In Group Theory written by K. W. Gruenberg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.




Homotopy Theoretic Methods In Group Cohomology


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.



Ergodic Theoretic Methods In Group Homology


Ergodic Theoretic Methods In Group Homology
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Author : Clara Löh
language : en
Publisher: Springer Nature
Release Date : 2020-03-14

Ergodic Theoretic Methods In Group Homology written by Clara Löh and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-14 with Mathematics categories.


This book offers a concise introduction to ergodic methods in group homology, with a particular focus on the computation of L2-Betti numbers. Group homology integrates group actions into homological structure. Coefficients based on probability measure preserving actions combine ergodic theory and homology. An example of such an interaction is provided by L2-Betti numbers: these invariants can be understood in terms of group homology with coefficients related to the group von Neumann algebra, via approximation by finite index subgroups, or via dynamical systems. In this way, L2-Betti numbers lead to orbit/measure equivalence invariants and measured group theory helps to compute L2-Betti numbers. Similar methods apply also to compute the rank gradient/cost of groups as well as the simplicial volume of manifolds. This book introduces L2-Betti numbers of groups at an elementary level and then develops the ergodic point of view, emphasising the connection with approximation phenomena for homological gradient invariants of groups and spaces. The text is an extended version of the lecture notes for a minicourse at the MSRI summer graduate school “Random and arithmetic structures in topology” and thus accessible to the graduate or advanced undergraduate students. Many examples and exercises illustrate the material.



Topological Methods In Group Theory


Topological Methods In Group Theory
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Author : Ross Geoghegan
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-17

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 2007-12-17 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.



Cohomological Methods In Homotopy Theory


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.