Pants decompositions of random surfaces

Details Pants decompositions of random surfaces Pants decompositions of random surfaces

2010-11-02

arxiv.org/abs/1011.0612v1

Mathematics

Geometric Topology

16 pages, 4 figures

Scientific paper

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 $g^{7/6 - \epsilon}$. 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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