Publikation: Equivariant cohomology, syzygies and orbit structure
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2014
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Transactions of the American Mathematical Society. 2014, 366(12), pp. 6567-6589. ISSN 0002-9947. eISSN 1088-6850. Available under: doi: 10.1090/S0002-9947-2014-06165-5
Zusammenfassung
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 HT*(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 Poincaré duality space if and only if the equivariant Poincaré pairing is perfect.
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ALLDAY, Christopher, Matthias FRANZ, Volker PUPPE, 2014. Equivariant cohomology, syzygies and orbit structure. In: Transactions of the American Mathematical Society. 2014, 366(12), pp. 6567-6589. ISSN 0002-9947. eISSN 1088-6850. Available under: doi: 10.1090/S0002-9947-2014-06165-5BibTex
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year={2014},
doi={10.1090/S0002-9947-2014-06165-5},
title={Equivariant cohomology, syzygies and orbit structure},
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}
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