Robert Bruner : From Groups to Cohomology to Varieties

Posted by , part of the Departmental Colloquium.

At

Nov. 11, 2005, 3 p.m.

In

SEO 636

Abstract

If we apply a generalized cohomology theory to the classifying space of a group, we obtain a ring whose structure reveals something about the group. As a first approximation we can consider the variety defined by this ring. The first result in this direction was the work of Quillen in 1971, describing the variety defined by the mod p cohomology in terms of the elementary abelian subgroups. A number of such results for other cohomology theories have now been proven. We shall review these and discuss in detail the case of connective K-theory, which provides a deformation from representation theory to cohomology (at the level of varieties) and speculate on generalizations of these results.