Classifying Spaces of Symmetric Groups and Wreath Products
Classifying Spaces of Symmetric Groups and Wreath Products

Author: David Louis Arnold

Publisher:

Published: 2013

Total Pages: 137

ISBN-13:

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This thesis was motivated by a desire to better understand the structure of classifying spaces of symmetric groups. The results contained in this thesis fall into two categories: general results about stable splittings, or the groups we will work with, and specific results about the stable splittings completed at the prime 2. We also present two examples involving linkage. It has been hypothesized that all linkage is strong linkage: we present a counter example. It was also thought that isomorphic summands of a classifying space would either all be linked in that space or all be linked in the spaces for some collection of subgroups. Again, we identify a counter example.

Group Cohomology and Algebraic Cycles
Group Cohomology and Algebraic Cycles

Author: Burt Totaro

Publisher: Cambridge University Press

Published: 2014-06-26

Total Pages: 245

ISBN-13: 1107015774

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This book presents a coherent suite of computational tools for the study of group cohomology algebraic cycles.

Classifying Spaces of Sporadic Groups
Classifying Spaces of Sporadic Groups

Author: David J. Benson

Publisher: American Mathematical Soc.

Published: 2008

Total Pages: 310

ISBN-13: 0821844741

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For each of the 26 sporadic finite simple groups, the authors construct a 2-completed classifying space using a homotopy decomposition in terms of classifying spaces of suitable 2-local subgroups. This construction leads to an additive decomposition of the mod 2 group cohomology.

Notes on Infinite Permutation Groups
Notes on Infinite Permutation Groups

Author: Meenaxi Bhattacharjee

Publisher: Springer Science & Business Media

Published: 1998-11-20

Total Pages: 224

ISBN-13: 9783540649656

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The book, based on a course of lectures by the authors at the Indian Institute of Technology, Guwahati, covers aspects of infinite permutation groups theory and some related model-theoretic constructions. There is basic background in both group theory and the necessary model theory, and the following topics are covered: transitivity and primitivity; symmetric groups and general linear groups; wreatch products; automorphism groups of various treelike objects; model-theoretic constructions for building structures with rich automorphism groups, the structure and classification of infinite primitive Jordan groups (surveyed); applications and open problems. With many examples and exercises, the book is intended primarily for a beginning graduate student in group theory.

Fusion Systems in Algebra and Topology
Fusion Systems in Algebra and Topology

Author: Michael Aschbacher

Publisher: Cambridge University Press

Published: 2011-08-25

Total Pages: 329

ISBN-13: 1107601002

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A fusion system over a p-group S is a category whose objects form the set of all subgroups of S, whose morphisms are certain injective group homomorphisms, and which satisfies axioms first formulated by Puig that are modelled on conjugacy relations in finite groups. The definition was originally motivated by representation theory, but fusion systems also have applications to local group theory and to homotopy theory. The connection with homotopy theory arises through classifying spaces which can be associated to fusion systems and which have many of the nice properties of p-completed classifying spaces of finite groups. Beginning with a detailed exposition of the foundational material, the authors then proceed to discuss the role of fusion systems in local finite group theory, homotopy theory and modular representation theory. This book serves as a basic reference and as an introduction to the field, particularly for students and other young mathematicians.

Cohomology of Finite Groups
Cohomology of Finite Groups

Author: Alejandro Adem

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 329

ISBN-13: 3662062801

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Some Historical Background This book deals with the cohomology of groups, particularly finite ones. Historically, the subject has been one of significant interaction between algebra and topology and has directly led to the creation of such important areas of mathematics as homo logical algebra and algebraic K-theory. It arose primarily in the 1920's and 1930's independently in number theory and topology. In topology the main focus was on the work ofH. Hopf, but B. Eckmann, S. Eilenberg, and S. MacLane (among others) made significant contributions. The main thrust of the early work here was to try to understand the meanings of the low dimensional homology groups of a space X. For example, if the universal cover of X was three connected, it was known that H2(X; A. ) depends only on the fundamental group of X. Group cohomology initially appeared to explain this dependence. In number theory, group cohomology arose as a natural device for describing the main theorems of class field theory and, in particular, for describing and analyzing the Brauer group of a field. It also arose naturally in the study of group extensions, N

Algebraic Topology
Algebraic Topology

Author: Carles Broto

Publisher: Springer Science & Business Media

Published: 1996-01-26

Total Pages: 424

ISBN-13: 9783764353339

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Central to this collection of papers are new developments in the general theory of localization of spaces. This field has undergone tremendous change of late and is yielding new insight into the mysteries of classical homotopy theory. The present volume comprises the refereed articles submitted at the Conference on Algebraic Topology held in Sant Feliu de Guíxols, Spain, in June 1994. Several comprehensive articles on general localization clarify the basic tools and give a report on the state of the art in the subject matter. The text is therefore accessible not only to the professional mathematician but also to the advanced student.

Algebraic Topology: Oaxtepec 1991
Algebraic Topology: Oaxtepec 1991

Author: Martin C. Tangora

Publisher: American Mathematical Soc.

Published: 1993

Total Pages: 504

ISBN-13: 0821851624

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This book consists of twenty-nine articles contributed by participants of the International Conference in Algebraic Topology held in July 1991 in Mexico. In addition to papers on current research, there are several surveys and expositions on the work of Mark Mahowald, whose sixtieth birthday was celebrated during the conference. The conference was truly international, with over 130 mathematicians from fifteen countries. It ended with a spectacular total eclipse of the sun, a photograph of which appears as the frontispiece. The papers range over much of algebraic topology and cross over into related areas, such as K theory, representation theory, and Lie groups. Also included is a chart of the Adams spectral sequence and a bibliography of Mahowald's publications.