Vol. 1, No. 4, 2019

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On the mod-$2$ cohomology of $\operatorname{SL}_3\bigl(\mathbb Z\bigl[\frac{1}{2},i\bigr]\bigr)$

Hans-Werner Henn

Vol. 1 (2019), No. 4, 539–560
Abstract

Let Γ = SL3([1 2,i]), let X be any mod-2 acyclic Γ-CW complex on which Γ acts with finite stabilizers and let Xs be the 2-singular locus of X. We calculate the mod-2 cohomology of the Borel construction of Xs 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; F2).

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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