Homological stability for symplectic groups via algebraic arc complexes
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915602411552768 |
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| author | Sierra, Ismael Wahl, Nathalie |
| author_facet | Sierra, Ismael Wahl, Nathalie |
| contents | We use algebraic arc complexes to prove a homological stability result for symplectic groups with slope 2/3 for rings with finite unitary stable rank. Symplectic groups are here interpreted as the automorphism groups of formed spaces with boundary, which are algebraic analogues of surfaces with boundary, that we also study in the present paper. Our stabilization map is a rank one stabilization in the category of formed spaces with boundary, going through both odd and even symplectic groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07895 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Homological stability for symplectic groups via algebraic arc complexes Sierra, Ismael Wahl, Nathalie Algebraic Topology We use algebraic arc complexes to prove a homological stability result for symplectic groups with slope 2/3 for rings with finite unitary stable rank. Symplectic groups are here interpreted as the automorphism groups of formed spaces with boundary, which are algebraic analogues of surfaces with boundary, that we also study in the present paper. Our stabilization map is a rank one stabilization in the category of formed spaces with boundary, going through both odd and even symplectic groups. |
| title | Homological stability for symplectic groups via algebraic arc complexes |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2411.07895 |