Exact cohomology sequences with integral coefficients for torus actions

2005/05/31 by Matthias Franz, Volker Puppe · 4 citations
Mathematics · #Advanced Operator Algebra Research #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:53D20 #msc:55N91

paper · pdf · doi:10.1007/s00031-005-1127-0

published as Transformation Groups 12 (2007), 65-76 · similar main result as in our preprint math.AT/0307112, but the proof is more elementary; 10 pages; final version

arxiv created 2006/09/10 · openalex publication_date 2006/12/28 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Using methods applied by Atiyah in equivariant K-theory, Bredon obtained exact sequences for the relative cohomologies (with rational coefficients) of the equivariant skeletons of (sufficiently nice) T-spaces, T=(S¹)ⁿ, with free equivariant cohomology over the cohomology of BT. Here we characterise those finite T-CW complexes with connected isotropy groups for which an analogous result holds with integral coefficients.

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