2006-10-13

Matthias Franz

Exact cohomology sequences for torus actions

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 "reasonable" 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.