Hugo Parlier

Publications (1)0 Total impact

• Source

  Available from: ArXiv

  Article: 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 $g^{7/6 - \epsilon}$. 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. Comment: 16 pages, 4 figures
  11/2010;