Homological stability for automorphisms of symmetric bilinear forms
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908867717234688 |
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| author | Nadig, Vikram |
| author_facet | Nadig, Vikram |
| contents | We establish homological stability for automorphisms of symmetric bilinear forms over a class of principal ideal domains that includes all fields, the integers, the Gaussian integers, and the Eisenstein integers. In conjunction with Grothendieck-Witt theoretic calculations, this determines a large part of the stable cohomology of the odd orthogonal groups $O_{\langle g,g \rangle}(\mathbb Z)$ in low degrees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13469 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homological stability for automorphisms of symmetric bilinear forms Nadig, Vikram Algebraic Topology Group Theory K-Theory and Homology We establish homological stability for automorphisms of symmetric bilinear forms over a class of principal ideal domains that includes all fields, the integers, the Gaussian integers, and the Eisenstein integers. In conjunction with Grothendieck-Witt theoretic calculations, this determines a large part of the stable cohomology of the odd orthogonal groups $O_{\langle g,g \rangle}(\mathbb Z)$ in low degrees. |
| title | Homological stability for automorphisms of symmetric bilinear forms |
| topic | Algebraic Topology Group Theory K-Theory and Homology |
| url | https://arxiv.org/abs/2512.13469 |