Publikation: Equivariant Poincaré–Alexander–Lefschetz duality and the Cohen–Macaulay property
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2014
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Algebraic & Geometric Topology. 2014, 14(3), pp. 1339-1375. ISSN 1472-2747. eISSN 1472-2739. Available under: doi: 10.2140/agt.2014.14.1339
Zusammenfassung
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.
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510 Mathematik
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torus actions, homology manifolds, equivariant homology, equivariant cohomology, Atiyah–Bredon complex, Poincaré–Alexander–Lefschetz duality, Cohen–Macaulay modules
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ALLDAY, Christopher, Matthias FRANZ, Volker PUPPE, 2014. Equivariant Poincaré–Alexander–Lefschetz duality and the Cohen–Macaulay property. In: Algebraic & Geometric Topology. 2014, 14(3), pp. 1339-1375. ISSN 1472-2747. eISSN 1472-2739. Available under: doi: 10.2140/agt.2014.14.1339BibTex
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title={Equivariant Poincaré–Alexander–Lefschetz duality and the Cohen–Macaulay property},
number={3},
volume={14},
issn={1472-2747},
journal={Algebraic & Geometric Topology},
pages={1339--1375},
author={Allday, Christopher and Franz, Matthias and Puppe, Volker}
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