Betti Numbers of Negatively Curved Orbifolds with Coefficients in Arbitrary Fields
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866912890596884480 |
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| author | Kapon, Guy Slutsky, Raz |
| author_facet | Kapon, Guy Slutsky, Raz |
| contents | We show that the Betti numbers of finite-volume negatively curved orbifolds grow at most linearly with the volume, with coefficients in an arbitrary field. In particular, this gives a linear bound for the Betti numbers of finite-volume hyperbolic orbifolds over $\mathbb{F}_p$. This extends a theorem of Gromov from manifolds to orbifolds in negative curvature, and answers a question of Samet, by strengthening his theorem from characteristic $0$ to arbitrary characteristic. The key new input is a quantitative bound on the homology of spherical quotients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08595 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Betti Numbers of Negatively Curved Orbifolds with Coefficients in Arbitrary Fields Kapon, Guy Slutsky, Raz Geometric Topology Group Theory We show that the Betti numbers of finite-volume negatively curved orbifolds grow at most linearly with the volume, with coefficients in an arbitrary field. In particular, this gives a linear bound for the Betti numbers of finite-volume hyperbolic orbifolds over $\mathbb{F}_p$. This extends a theorem of Gromov from manifolds to orbifolds in negative curvature, and answers a question of Samet, by strengthening his theorem from characteristic $0$ to arbitrary characteristic. The key new input is a quantitative bound on the homology of spherical quotients. |
| title | Betti Numbers of Negatively Curved Orbifolds with Coefficients in Arbitrary Fields |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2602.08595 |