Pants decompositions of random surfaces

Larry Guth; Hugo Parlier; Robert Young

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arXiv · 1011.0612

Pants decompositions of random surfaces

Larry Guth·Hugo Parlier·Robert Young

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Abstract

Our goal is to show, in two different contexts, that "random" surfaces have large pants decompositions. First we show that there are hyperbolic surfaces of genus $g$ for which any pants decomposition requires curves of total length at least $g^{7/6 - ε}$. Moreover, we prove that this bound holds for most metrics in the moduli space of hyperbolic metrics equipped with the Weil-Petersson volume form. We then consider surfaces obtained by randomly gluing euclidean triangles (with unit side length) together and show that these surfaces have the same property.

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Larry Guth, Hugo Parlier, Robert Young. 2010-11-02. Pants decompositions of random surfaces. https://arxiv.org/abs/1011.0612

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