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arXiv · 0808.0625

The third homology of the special linear group of a field

Kevin Hutchinson·Liqun Tao
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Abstract

We prove that for any infinite field homology stability for the third integral homology of the special linear groups $SL(n,F)$ begins at $n=3$. When $n=2$ the cokernel of the map from the third homology of $SL(2,F)$ to the third homology of $SL(3,F)$ is naturally isomorphic to the square of Milnor $K_3$. We discuss applications to the indecomposable $K_3$ of the field and to Milnor-Witt K-theory.

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Kevin Hutchinson, Liqun Tao. 2008-08-05. The third homology of the special linear group of a field. https://arxiv.org/abs/0808.0625

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