Mirzakhani's Curve Counting: From Simple to All

Viveka Erlandsson; Juan Souto

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arXiv · 1904.05091

Mirzakhani's Curve Counting: From Simple to All

Viveka Erlandsson·Juan Souto

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Abstract

Mirzakhani obtained the asymptotic growth, when $L\to\infty$, of the number of curves in the mapping class group orbit of some given simple curve and with length at most $L$. Years later she extended this result from simple to arbitrary curves. Here we give a short and relative low-tech argument showing how to derive the general result from the one for simple curves.

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Viveka Erlandsson, Juan Souto. 2019-04-10. Mirzakhani's Curve Counting: From Simple to All. https://arxiv.org/abs/1904.05091

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