Homotopy invariance for homology of linear groups

Details Homotopy invariance for homology of linear groups Homotopy invariance for homology of linear groups

2010-11-23

arxiv.org/abs/1011.5110v4

Mathematics

K-Theory and Homology

13 pages, small revision,added application to degree 3 case of Friedlander-Milnor conjecture

Scientific paper

This note explains how to prove that for any simply-connected reductive group G and any infinite field k, the inclusion of k in k[t] induces an isomorphism on homology. This generalizes results of Soule and Knudson. The result can be used to deduce the degree 3 case of the Friedlander-Milnor conjecture for simply-connected Chevalley groups of rank at least 2, using Morel's A^1-homotopy approach.

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