Volume 14, issue 3 (2014)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 20, 1 issue

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

Author Index
The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
To Appear
Other MSP Journals
Equivariant Poincaré–Alexander–Lefschetz duality and the Cohen–Macaulay property

Christopher Allday, Matthias Franz and Volker Puppe

Algebraic & Geometric Topology 14 (2014) 1339–1375

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.

torus actions, homology manifolds, equivariant homology, equivariant cohomology, Atiyah–Bredon complex, Poincaré–Alexander–Lefschetz duality, Cohen–Macaulay modules
Mathematical Subject Classification 2010
Primary: 55N91
Secondary: 13C14, 57R91
Received: 30 March 2013
Revised: 16 September 2013
Accepted: 30 September 2013
Published: 7 April 2014
Christopher Allday
Department of Mathematics
University of Hawaii
2565 McCarthy Mall
Honolulu, HI 96822
Matthias Franz
Department of Mathematics
University of Western Ontario
London, ON N6A 5B7
Volker Puppe
Fachbereich Mathematik und Statistik
Universität Konstanz
D-78457 Konstanz