Topology Seminar: Anssi Lahtinen

In this talk, I will discuss a surprising connection between finite groups of Lie type and string topology of classifying spaces of compact connected Lie groups recently discovered by Jesper Grodal and myself: the cohomology of a finite group of Lie type is a module over the cohomology of the free loop space of the classifying space of the corresponding compact Lie group when the latter cohomology groups are equipped with a string topological multiplication. This module structure provides in particular a new perspective towards the Tezuka conjecture asserting that under certain conditions, the cohomologies of the two objects are isomorphic.