Stable moduli spaces of hermitian forms
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866916689275256832 |
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| author | Hebestreit, Fabian Steimle, Wolfgang |
| author_facet | Hebestreit, Fabian Steimle, Wolfgang |
| contents | We prove that Grothendieck-Witt spaces of Poincaré 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 Calmès, 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 Poincaré category as the homotopy type of the associated cobordism category. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_13911 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Stable moduli spaces of hermitian forms Hebestreit, Fabian Steimle, Wolfgang K-Theory and Homology Algebraic Topology 11E70, 19G38, 20J06 We prove that Grothendieck-Witt spaces of Poincaré 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 Calmès, 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 Poincaré category as the homotopy type of the associated cobordism category. |
| title | Stable moduli spaces of hermitian forms |
| topic | K-Theory and Homology Algebraic Topology 11E70, 19G38, 20J06 |
| url | https://arxiv.org/abs/2103.13911 |