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Homotopy invariance for homology of linear groups: the case SL_4

In this paper, we investigate homotopy invariance for homology of SL_4. For any commutative ring, the group E_4(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.

preprint2011arXivOpen access
Matthias Wendt
math.KT
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Matthias Wendt

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