A homotopy theoretic approach to fusion systems: p-local group theory

Ran Levi (U Aberdeen)

Wednesday 17th October, 2012 16:00-17:00 516

Abstract

Fusion systems were introduced by Ll. Puig in the early 1990s as a tool for a conceptual study of the classification problem of finite simple groups. They concept broke thr boundaries of group theory with its utilisation in the theory of p-local finite and compact groups by Broto-Levi-Oliver. In particular it was shown recently by Chermak, and with a different proof by Oliver, that every saturated fusion system over a finite p-group has a unique associated "classifying space". (This statement appears to hold in fact in even greater generality.) Thus one has a direct correspondence between algebraic phenomena in fusions systems and analogous phenomena in their classifying spaces. In this talk we will give a brief survey of what is known in the theory of p-local groups, and indicate current and potential future direction of research in the subject.

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