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arXiv · 2111.01539

The third homology of symplectic groups and algebraic K-theory

Marco Schlichting·Husney Parvez Sarwar
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Abstract

We improve the homology stability range for the 3rd integral homology of symplectic groups over commutative local rings with infinite residue field. As an application, we show that for local commutative rings containing an infinite field of characteristic not 2 the symbol map from Milnor-Witt K-theory to higher Grothendieck-Witt groups is an isomorphism in degrees 2 and 3.

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Marco Schlichting, Husney Parvez Sarwar. 2021-11-02. The third homology of symplectic groups and algebraic K-theory. https://arxiv.org/abs/2111.01539

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