Homotopy invariance for homology of linear groups: the case SL_4

Abstract

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.

arXiv commentThe paper has been withdrawn. Due to counterexamples in the case SL_3 I no longer believe the claims made in this paper are correct, although I am unable to spot the crucial mistake