On the mod-2 cohomology of SL3ℤ,i

Let $Γ = {SL}_{3} (ℤ [\frac{1}{2}, i])$ , let $X$ be any mod- $2$ acyclic $Γ$ -CW complex on which $Γ$ acts with finite stabilizers and let $X_{s}$ be the $2$ -singular locus of $X$ . We calculate the mod- $2$ cohomology of the Borel construction of $X_{s}$ with respect to the action of $Γ$ . This cohomology coincides with the mod- $2$ cohomology of $Γ$ in cohomological degrees bigger than $8$ and the result is compatible with a conjecture of Quillen which predicts the structure of the cohomology ring $H^{*} (Γ; F_{2})$ .

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Keywords

cohomology of special and general linear groups, Quillen conjecture

Mathematical Subject Classification 2010

Primary: 20G10

Secondary: 55R40

Milestones

Received: 29 January 2018

Revised: 6 August 2018

Accepted: 20 August 2018

Published: 14 December 2018

Authors

Hans-Werner Henn
Institut de Recherche Mathématique Avancée C.N.R.S., Université de Strasbourg France

Vol. 1, No. 4, 2019

Hans-Werner Henn

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors