Counting geodesics of given commutator length

Viveka Erlandsson; Juan Souto

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arXiv · 2304.10274

Counting geodesics of given commutator length

Viveka Erlandsson·Juan Souto

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Abstract

Let $\Sigma$ be a closed hyperbolic surface. We study, for fixed $g$, the asymptotics of the number of those periodic geodesics in $\Sigma$ having at most length $L$ and which can be written as the product of $g$ commutators. The basic idea is to reduce these results to being able to count critical realizations of trivalent graphs in $\Sigma$. In the appendix we use the same strategy to give a proof of Huber's geometric prime number theorem.

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Viveka Erlandsson, Juan Souto. 2023-04-20. Counting geodesics of given commutator length. https://arxiv.org/abs/2304.10274

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