Counting hyperbolic 4-manifolds with vanishing Seiberg-Witten invariants

Kaixu Zhang

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arXiv · 2508.13464

Counting hyperbolic 4-manifolds with vanishing Seiberg-Witten invariants

Kaixu Zhang

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Abstract

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.

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Kaixu Zhang. 2025-08-19. Counting hyperbolic 4-manifolds with vanishing Seiberg-Witten invariants. https://arxiv.org/abs/2508.13464

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