Fusion Systems in Algebra and Topology

Released on by Michael Aschbacher
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  • Fusion Systems in Algebra and Topology Book Detail

  • Author : Michael Aschbacher
  • Release Date : 2011-08-25
  • Publisher : Cambridge University Press
  • Genre : Mathematics
  • Pages : 329
  • ISBN 13 : 1107601002
  • File Size : 96,96 MB
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Fusion Systems in Algebra and Topology by Michael Aschbacher PDF Summary

Book Description: 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.

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The study of fusion first arose in the local theory of finite groups. Puig abstracted the fusion data of a finite group to the notion of fusion system, an objec

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This monograph provides a comprehensive treatment of the classification of small fusion systems, that is, fusion systems with few essential subgroups. It demons