%0 Journal Article
%T Equivariant cohomology, syzygies and orbit structure
%A Christopher Allday
%A Matthias Franz
%A Volker Puppe
%J Mathematics
%D 2011
%I arXiv
%R 10.1090/S0002-9947-2014-06165-5
%X Let X be a "nice" space with an action of a torus T. We consider the Atiyah-Bredon sequence of equivariant cohomology modules arising from the filtration of X by orbit dimension. We show that a front piece of this sequence is exact if and only if the H^*(BT)-module H_T^*(X) is a certain syzygy. Moreover, we express the cohomology of that sequence as an Ext module involving a suitably defined equivariant homology of X. One consequence is that the GKM method for computing equivariant cohomology applies to a Poincare duality space if and only if the equivariant Poincare pairing is perfect.
%U http://arxiv.org/abs/1111.0957v2