Pants Decompositions of Random Surfaces

Guth, Larry; Parlier, Hugo; Young, Robert

doi:10.1007/s00039-011-0131-x

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Journal article

Pants Decompositions of Random Surfaces

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Guth, Larry Department of Mathematics, University of Toronto, Bahen Centre, 40 St. George St., M5S 2E4, Toronto, Ontario, Canada
Parlier, Hugo Department of Mathematics, University of Fribourg, Chemin du Musée 23, CH-1700, Fribourg, Switzerland
Young, Robert Courant Institute of Mathematical Sciences, 251 Mercer St., 10012, New York, NY, USA

2011

Published in:

Geometric and Functional Analysis. - SP Birkhäuser Verlag Basel. - 2011, vol. 21, no. 5, p. 1069-1090

English 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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