**SMS scnews item created by James East at Tue 21 Jul 2009 1020**

Type: Seminar

Distribution: World

Expiry: 24 Jul 2009

**Calendar1: 24 Jul 2009 1205-1255**

**CalLoc1: Carslaw 375**

Auth: jamese@bari.maths.usyd.edu.au

### Algebra Seminar

# Arc spaces and equivariant cohomology

### Alan Stapledon

#### Friday July 24, 12:05--12:55pm, Carslaw 375

###### Abstract

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_{\infty} 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.

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After the seminar we will take the speaker to lunch.

See the Algebra Seminar web page for information about other seminars in the series.

James East jamese@maths.usyd.edu.au