Equivariant Poincaré–Alexander–Lefschetz duality and the Cohen–Macaulay property

Allday, Christopher¹ ; Franz, Matthias² ; Puppe, Volker³

¹Department of Mathematics, University of Hawaii, 2565 McCarthy Mall, Honolulu, HI 96822, USA
²Department of Mathematics, University of Western Ontario, London, ON N6A 5B7, Canada
³Fachbereich Mathematik und Statistik, Universität Konstanz, D-78457 Konstanz, Germany

Algebraic and Geometric Topology, Tome 14 (2014) no. 3, pp. 1339-1375

Résumé

We prove a Poincaré–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.

Détail

DOI : 10.2140/agt.2014.14.1339

Classification : 55N91, 13C14, 57R91
Keywords: torus actions, homology manifolds, equivariant homology, equivariant cohomology, Atiyah–Bredon complex, Poincaré–Alexander–Lefschetz duality, Cohen–Macaulay modules

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