Abstract: The GKM method is a powerful way to compute the equivariant (and ordinary) cohomology of many spaces with torus actions. So far it has been applied to so-called equivariantly formal $T$-spaces, which include compact Hamiltonian $T$-manifolds.

In this talk I will explain that the GKM method is valid for a much larger class of $T$-spaces. The explanation is based on a new interpretation of a sequence originally due to Atiyah and Bredon, and involves the notion of syzygies as used in commutative algebra. I will also exhibit a surprising relation between the equivariant Poincaré pairing and the GKM description.

This is joint work with Chris Allday and Volker Puppe.