Homotopy invariance for homology of linear groups: the case SL4
Abstract
In this paper, we investigate homotopy invariance for homology of SL4. For any commutative ring, the group E4(R[t]) acts on a simplicial complex whose contractibility implies homotopy invariance. We show that for a local factorial ring R, this complex satisfies the CAT(0)-property for the induced length metric from the Bruhat-Tits building.
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