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arXiv · 2103.13911

Stable moduli spaces of hermitian forms

Fabian Hebestreit·Wolfgang Steimle
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Abstract

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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Fabian Hebestreit, Wolfgang Steimle. 2021-03-25. Stable moduli spaces of hermitian forms. https://doi.org/10.1017/fmp.2026.10032

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