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Equivariant
Poincaré–Alexander–Lefschetz duality and the Cohen–Macaulay
property
Christopher Allday, Matthias Franz and Volker Puppe |
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Algebraic & Geometric Topology 14 (2014) 1339–1375
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Abstract |
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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. |
Keywords
torus actions, homology manifolds, equivariant homology,
equivariant cohomology, Atiyah–Bredon complex,
Poincaré–Alexander–Lefschetz duality, Cohen–Macaulay
modules
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Mathematical Subject Classification 2010
Primary: 55N91
Secondary: 13C14, 57R91
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References |
Publication
Received: 30 March 2013
Revised: 16 September 2013
Accepted: 30 September 2013
Published: 7 April 2014
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Authors |
| Christopher Allday | |
| Department of Mathematics University of Hawaii 2565 McCarthy Mall Honolulu, HI 96822 USA |
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| Matthias Franz | |
| Department of Mathematics University of Western Ontario London, ON N6A 5B7 Canada |
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| http://www.math.uwo.ca/~mfranz/ | |
| Volker Puppe | |
| Fachbereich Mathematik und
Statistik Universität Konstanz D-78457 Konstanz Germany |
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