Fusion action systems by Matthew J.K. Gelvin.
Name
681918282-MIT.pdf
Description
Full printable version
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6.42 MB
Format
Adobe PDF
Checksum (MD5)
8b297a9a98611f26fc517e3e6397d344
Author(s)
Gelvin, Matthew J. K. (Matthew Justin Karcher)
Advisor(s)
Haynes Miller.
Date Issued
2010
Publisher
Massachusetts Institute of Technology
Abstract
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 object that reflects local data in more abstract algebraic settings, such as the block theory of finite groups. Martino and Priddy conjectured that the algebraic data of a fusion system of a finite group should have a topological interpretation, which result was proved by Oliver using the notion of p-local finite group introduced by the team of Broto, Levi, and Oliver. The study of fusion systems and p-local finite groups thus provides a bridge between algebraic fields related to local group theory and algebraic topology. In this thesis we generalize the notion of abstract fusion system to model the local structure of a group action on a finite set. The resulting fusion action systems can be seen as a generalization of the notion of abstract fusion system, though we describe other possible interpretations as well. We also develop the notion of a p-local finite group action, which allows for connections between fusion action system theory and algebraic topology..
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 131-132).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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