Fusion systems in algebra and topology / Michael Aschbacher, Radha Kessar, Bob Oliver.

Format:

Book

Author/Creator:

Aschbacher, Michael, 1944- author.

Kessar, Radha, author.

Oliver, Robert, 1949- author.

Series:

London Mathematical Society lecture note series ; 391.

London Mathematical Society lecture note series ; 391

Language:

English

Subjects (All):

Combinatorial group theory.

Topological groups.

Algebraic topology.

Physical Description:

1 online resource (vi, 320 pages) : digital, PDF file(s).

Edition:

1st ed.

Other Title:

Fusion Systems in Algebra & Topology

Place of Publication:

Cambridge : Cambridge University Press, 2011.

Language Note:

English

Summary:

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.

Contents:

Introduction to fusion systems

The local theory of fusion systems

Fusion and homotopy theory

Fusion and representation theory

Appendix A. Background facts about groups.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-107-23223-6

1-139-10184-6

1-139-10364-4

1-299-40566-5

1-139-10118-8

1-139-09916-7

1-139-00384-4

OCLC:

826452027