EQUIVARIANT COHOMOLOGY, SYZYGIES AND ORBIT STRUCTURE

作者：Allday Christopher^*; Franz Matthias; Puppe Volker

来源：Transactions of the American Mathematical Society, 2014, 366(12): 6567-6589.

DOI：10.1090/S0002-9947-2014-06165-5

Let X be a %26quot;nice%26quot; 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. %26lt;br%26gt;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.

• 出版日期2014-12