Equivariant cohomology, syzygies and orbit structure
Algebraic Topology
2014-10-24 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1111.0957,
title = {Equivariant cohomology, syzygies and orbit structure},
author = {Christopher Allday and Matthias Franz and Volker Puppe},
journal= {arXiv preprint arXiv:1111.0957},
year = {2014}
}
Comments
23 pages. The former Section 6 has been substantially expanded and is now a separate paper, see arXiv:1303.1146. Several minor changes