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Fusion Systems in Algebra and Topology

Aschbacher, Michael and Kessar, Radha and Oliver, Bob (2011) Fusion Systems in Algebra and Topology. London Mathematical Society Lecture Note Series. No.391. Cambridge University Press , Cambridge. ISBN 9781139003841. http://resolver.caltech.edu/CaltechAUTHORS:20180807-124803752

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Abstract

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.


Item Type:Book
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https://doi.org/10.1017/CBO9781139003841DOIBook Publisher
Additional Information:© 2011 Cambridge University Press.
Record Number:CaltechAUTHORS:20180807-124803752
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180807-124803752
Official Citation:Aschbacher, M., Kessar, R., & Oliver, B. (2011). Fusion Systems in Algebra and Topology (London Mathematical Society Lecture Note Series). Cambridge: Cambridge University Press. doi:10.1017/CBO9781139003841
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:88625
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:07 Aug 2018 20:01
Last Modified:07 Aug 2018 20:01

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