Equivariant Poincar\'e-Alexander-Lefschetz duality and the Cohen-Macaulay property
Abstract
We prove a Poincare-Alexander-Lefschetz duality theorem for rational torus-equivariant cohomology and rational homology manifolds. We allow non-compact and non-orientable spaces. We use this to deduce certain short exact sequences in equivariant cohomology, originally due to Duflot in the differentiable case, from similar, but more general short exact sequences in equivariant homology. A crucial role is played by the Cohen-Macaulayness of relative equivariant cohomology modules arising from the orbit filtration.
Keywords
Cite
@article{arxiv.1303.1146,
title = {Equivariant Poincar\'e-Alexander-Lefschetz duality and the Cohen-Macaulay property},
author = {Christopher Allday and Matthias Franz and Volker Puppe},
journal= {arXiv preprint arXiv:1303.1146},
year = {2014}
}
Comments
28 pages. This is a substantially expanded version of Section 6 of arXiv:1111.0957v1. v2: new result (Prop. 2.7) about equivariant homology in the case of freely acting subgroups; minor changes. v3: mistake in the proof of Prop. 2.7 corrected