Equivariant cohomology, syzygies and orbit structure


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ALLDAY, Christopher, Matthias FRANZ, Volker PUPPE, 2014. Equivariant cohomology, syzygies and orbit structure. In: Transactions of the American Mathematical Society. 366(12), pp. 6567-6589. ISSN 0002-9947. eISSN 1088-6850

@article{Allday2014Equiv-30191, title={Equivariant cohomology, syzygies and orbit structure}, year={2014}, doi={10.1090/S0002-9947-2014-06165-5}, number={12}, volume={366}, issn={0002-9947}, journal={Transactions of the American Mathematical Society}, pages={6567--6589}, author={Allday, Christopher and Franz, Matthias and Puppe, Volker} }

Equivariant cohomology, syzygies and orbit structure Franz, Matthias 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<sub>T</sub>*(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.<br />One consequence is that the GKM method for computing equivariant cohomology applies to a Poincaré duality space if and only if the equivariant Poincaré pairing is perfect. Puppe, Volker Puppe, Volker Allday, Christopher Allday, Christopher 2014 Franz, Matthias 2015-03-11T09:19:54Z 2015-03-11T09:19:54Z eng

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