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arXiv · 1111.0957

Equivariant cohomology, syzygies and orbit structure

Christopher Allday·Matthias Franz·Volker Puppe
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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.

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Christopher Allday, Matthias Franz, Volker Puppe. 2011-11-03. Equivariant cohomology, syzygies and orbit structure. https://doi.org/10.1090/s0002-9947-2014-06165-5

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