Counting hyperbolic 4-manifolds with vanishing Seiberg-Witten invariants
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911110983057408 |
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| author | Zhang, Kaixu |
| author_facet | Zhang, Kaixu |
| contents | Ian Agol and Francesco Lin proved the existence of hyperbolic four-manifolds with vanishing Seiberg-Witten invariants. We prove that the number of such manifolds of volume at most $v$ is asymptotically bounded by $v^{cv}$ considered up to commensurability, which has the same form as the lower bound and upper bound of the number of hyperbolic four-manifolds of volume at most $v$ proved by Tsachik Gelander and Arie Levit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13464 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Counting hyperbolic 4-manifolds with vanishing Seiberg-Witten invariants Zhang, Kaixu Geometric Topology Primary 57K41, Secondary 57M50 Ian Agol and Francesco Lin proved the existence of hyperbolic four-manifolds with vanishing Seiberg-Witten invariants. We prove that the number of such manifolds of volume at most $v$ is asymptotically bounded by $v^{cv}$ considered up to commensurability, which has the same form as the lower bound and upper bound of the number of hyperbolic four-manifolds of volume at most $v$ proved by Tsachik Gelander and Arie Levit. |
| title | Counting hyperbolic 4-manifolds with vanishing Seiberg-Witten invariants |
| topic | Geometric Topology Primary 57K41, Secondary 57M50 |
| url | https://arxiv.org/abs/2508.13464 |