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Stable moduli spaces of hermitian forms

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arxiv 2103.13911 v5 pith:PCVCZSXB submitted 2021-03-25 math.KT math.AT

Fabian Hebestreit , Wolfgang Steimle This is my paper · ORCID
classification math.KTmath.AT
keywords hermitiangrothendieck-wittspacescategoriescategorycobordismformsmoduli
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We prove that Grothendieck-Witt spaces of Poincar\'e categories are, in many cases, group completions of certain moduli spaces of hermitian forms. This, in particular, identifies Karoubi's classical hermitian and quadratic K-groups with the genuine Grothendieck-Witt groups from our joint work with Calm\`es, Dotto, Harpaz, Land, Moi, Nardin and Nikolaus, and thereby completes our solution of several conjectures in hermitian K-theory. The method of proof is abstracted from work of Galatius and Randal-Williams on cobordism categories of manifolds using the identification of the Grothendieck-Witt space of a Poincar\'e category as the homotopy type of the associated cobordism category.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Chromatic Purity in Hermitian K-Theory at $p=2$

    math.KT 2025-01 reject novelty 6.0 of 10

    At p=2, L-theory of rings with anti-involution is claimed to have no chromatic redshift and to satisfy a chromatic purity theorem.

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