What is equivariant cohomology and what is it good for?

Peter May

University of Chicago

Brandeis University

Thursday, May 3, 2012

Talk at 4:30 p.m. in 317 Goldsmith Hall

Tea at 4:00 p.m. in 300 Goldsmith Hall

Abstract: Let G be a topological group and let G act on a space X. What can one deduce about the G-fixed point space X^G and the orbit space X/G from information about X? I will explain classical cohomological results, P.A. Smith theory and the Connor conjecture, that give quite remarkable answers to these questions. I will use modern proofs of these results to describe equivariant cohomology theory, which means different things to different people. The proof of the Connor conjecture will lead us directly to the idea that cohomology should be graded on the real representation ring of G rather than just on the integers. In turn, this will lead us to a remarkable relationship between Mackey functors in algebra and equivariant stable homotopy groups. All concepts will be defined.

Home Web page: Alexandru I. Suciu Posted: April 21, 2012
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