Some hermitian K-groups via geometric topology

Krannich, Manuel; Kupers, Alexander

doi:10.1090/proc/15098

Some hermitian K-groups via geometric topology
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by Manuel Krannich and Alexander Kupers PDF

Proc. Amer. Math. Soc. 149 (2021), 2745-2752 Request permission

Abstract:

We compute the first two symplectic quadratic K-theory groups of the integers, or equivalently, the first two stable homology groups of the group of symplectic integral matrices preserving the standard quadratic refinement. The main novelty in our calculation lies in its method, which is based on high-dimensional manifold theory.

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