## 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.