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arxiv: 2002.05255 · v2 · pith:5FMBV7DK · submitted 2020-02-12 · math.AT · math.KT

Some Hermitian K-groups via geometric topology

Manuel Krannich , Alexander Kupers This is my paper

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classification math.AT math.KT
keywords firstgroupsquadraticsymplecticcalculationcomputeequivalentlygeometric
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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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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Hermitian K-theory for stable $\infty$-categories III: Grothendieck-Witt groups of rings

    math.KT 2020-09 unverdicted novelty 7.0

    A new fibre sequence relates classical Grothendieck-Witt groups to K-theory orbits and symmetric L-theory, enabling removal of the 2-unit assumption and resolution of multiple open problems for Dedekind rings and numb...