University of Sydney Algebra Seminar

Alan Stapledon (University of Michigan)

Friday 24th July, 12.05-12.55pm, Carslaw 375

Arc spaces and equivariant cohomology

We present a new geometric interpretation of equivariant cohomology in which one replaces a smooth, complex G-variety X by its associated arc space J_∞ X, with its induced G-action. This not only allows us to obtain geometric classes in equivariant cohomology of arbitrarily high degree, but also provides more flexibility for equivariantly deforming classes and geometrically interpreting multiplication in the equivariant cohomology ring. As applications, we present geometric Z-bases for the equivariant cohomology ring of a smooth toric variety and the equivariant cohomology ring of the general linear group acting on a point.