2009-04-03
Alimjon Eshmatov, Cornell University
Equivariant cohomology of conjugation spaces
In 1953 paper, Borel noted that there is a degree-halving ring isomorphism from the cohomology ring of complex flags in $\mathbb{C}^n$
to the cohomology ring of real flags in $\mathbb{R}^n$. Later, in joint work with Haefliger they studied a broader class of topological
spaces with similar behavior. But it was only recently in work of Hausmann-Holm-Puppe, they have been axiomatized.
I will define conjugation spaces (following Hausmann-Holm-Puppe) and explain some of their properties with some simple examples. At the
end I will discuss some results on equivariant cohomology of these spaces.