Teichm\"uller theory via random simple closed curves

Curtis T. McMullen; Tina Torkaman

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arXiv · 2512.14101

Teichm\"uller theory via random simple closed curves

Curtis T. McMullen·Tina Torkaman

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Abstract

We show the map $\sigma : T_g \to C_g$ sending a compact hyperbolic surface $X$ to a random simple closed geodesic on $X$ determines a proper embedding of Teichm\"uller space into the space of geodesic currents. The proof depends on a formula for the intersection number $i(C,C')$ of a pair of multicurves, expressed in terms of Dehn coordinates on $ML_g(\mathbb{Z})$.

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BibTeX RIS

Curtis T. McMullen, Tina Torkaman. 2025-12-16. Teichm\"uller theory via random simple closed curves. https://arxiv.org/abs/2512.14101

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