# An application of group theory to topology

Wed, 07/12/2016 - 10:30

Speaker:

Prof. George Glauberman (University of Chicago)

Seminar:

Place:

Third floor seminar room

Abstract:

Let p be a prime. To every finite group is associated a topological

space known as the p-completion of its classifying space. The

Martino-Priddy conjecture states that for two groups G and H, these

spaces are homotopically equivalent if and only if there is a special

type of isomorphism between the Sylow p-subgroups of G and H

(an isomorphism of fusion systems, e.g., elements conjugate in G

are mapped to elements conjugate in H).

The combined work of several authors has proved this conjecture

and some extensions, partly by assuming the classification of

finite simple groups. Recently, J. Lynd and I removed this assumption.

I plan to discuss the main ideas of these results.

- Last modified: 26/11/2016