Exact sequences for equivariantly formal spaces
Matthias Franz, Volker Puppe

TL;DR
This paper generalizes the Atiyah-Bredon exact sequence for equivariantly formal spaces, extending its applicability to various coefficients and actions without fixed points, thereby broadening the theoretical framework of equivariant cohomology.
Contribution
It introduces a generalized exact sequence for equivariantly formal spaces with broader coefficients and actions without fixed points, extending previous results.
Findings
Generalized Atiyah-Bredon sequence for various coefficients
Extended sequence applicable to fixed point free actions
Broadened theoretical framework for equivariant cohomology
Abstract
Let T be a torus. We present an exact sequence relating the relative equivariant cohomologies of the skeletons of an equivariantly formal T-space. This sequence, which goes back to Atiyah and Bredon, generalizes the so-called Chang-Skjelbred lemma. As coefficients, we allow prime fields and subrings of the rationals, including the integers. We extend to the same coefficients a generalization of this "Atiyah-Bredon sequence" for actions without fixed points which has recently been obtained by Goertsches and Toeben.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology
