2013/03/31 by Christopher Allday, Matthias Franz, Volker Puppe · 8 citations
Mathematics · #Advanced Combinatorial Mathematics #Cohomology #Differentiable function #Duality (order theory) #Equivariant cohomology #Equivariant map #Geometric and Algebraic Topology #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Property (philosophy) #math.AT #msc:13C14 #msc:55N91 #msc:57R91
paper · pdf · doi:10.2140/agt.2014.14.1339
published in Algebraic & Geometric Topology 14(3), 1339-1375 (Mathematical Sciences Publishers) · 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
arxiv created 2013/09/15 · openalex publication_date 2014/04/07 · arxiv updated 2014/09/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We prove a Poincar-Alexander-Lefschetz duality theorem for rational torus-equivariant cohomology and rational homology manifolds. We allow non-compact and nonorientable 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.