Statistics of finite degree covers of torus knot complements

Elizabeth Baker; Bram Petri

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arXiv · 2005.11956

Statistics of finite degree covers of torus knot complements

Elizabeth Baker·Bram Petri

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Abstract

In the first part of this paper, we determine the asymptotic subgroup growth of the fundamental group of a torus knot complement. In the second part, we use this to study random finite degree covers of torus knot complements. We determine their Benjamini-Schramm limit and the linear growth rate of the Betti numbers of these covers. All these results generalise to a larger class of lattices in $\mathrm{PSL}(2,\mathbb{R})\times \mathbb{R}$. As a by-product of our proofs, we obtain analogous limit theorems for high degree random covers of non-uniform Fuchsian lattices with torsion.

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BibTeX RIS

Elizabeth Baker, Bram Petri. 2020-05-25. Statistics of finite degree covers of torus knot complements. https://arxiv.org/abs/2005.11956

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