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arXiv · 1702.05032

On the Mod-2 Cohomology of SL 3 (z[ 1 2 , i])

Hans-Werner Henn
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Abstract

Let $Γ$ = SL 3 (Z[ 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 constructon 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 strucure of the cohomology ring H * ($Γ$; Z/2).

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Hans-Werner Henn. 2018-01-30. On the Mod-2 Cohomology of SL 3 (z[ 1 2 , i]). https://doi.org/10.2140/tunis.2019.1.539

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