Counting Curves in Hyperbolic Surfaces

Viveka Erlandsson; Juan Souto

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arXiv · 1508.02265

Counting Curves in Hyperbolic Surfaces

Viveka Erlandsson·Juan Souto

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Abstract

Let $\Sigma$ be a hyperbolic surface. We study the set of curves on $\Sigma$ of a given type, i.e. in the mapping class group orbit of some fixed but otherwise arbitrary $\gamma_0$. For example, in the particular case that $\Sigma$ is a once-punctured torus, we prove that the cardinality of the set of curves of type $\gamma_0$ and of at most length $L$ is asymptotic to $L^2$ times a constant.

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Viveka Erlandsson, Juan Souto. 2015-08-10. Counting Curves in Hyperbolic Surfaces. https://arxiv.org/abs/1508.02265

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