# University of Toronto's Symplectic Geometry Seminar

October 11, 2006, 2:10pm

SS 2128

## Matthias Franz

### University of Geneva

## Exact cohomology sequences for torus actions

**Abstract: **In many interesting cases, the equivariant cohomology (with real
coefficients) of a Hamiltonian T-manifold can be computed from the
associated moment graph, which encodes information about the fixed
points and the one-dimensional orbits. This can be seen as an
application of the Chang-Skjelbred lemma, which for any "resonable"
T-space X describes the image of the equivariant cohomology of X
in that of the fixed point set, provided that X is equivariantly
formal. A more general, but less known result is due to Atiyah
and Bredon.
In this talk I will present versions of the Chang-Skjelbred lemma
and the Atiyah-Bredon theorem valid for integer coefficients, and
I will illustrate them by several examples.