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15 July 2013 The diameter of the thick part of moduli space and simultaneous Whitehead moves
Kasra Rafi, Jing Tao
Duke Math. J. 162(10): 1833-1876 (15 July 2013). DOI: 10.1215/00127094-2323128

Abstract

Let S be a surface of genus g with p punctures with negative Euler characteristic. We study the diameter of the ϵ-thick part of moduli space of S equipped with the Teichmüller or Thurston’s Lipschitz metric. We show that the asymptotic behaviors in both metrics are of order log(g+pϵ). The same result also holds for the ϵ-thick part of the moduli space of metric graphs of rank n equipped with the Lipschitz metric. The proof involves a sorting algorithm that sorts an arbitrarily labeled tree with n labels using simultaneous Whitehead moves, where the number of steps is of order log(n). As a related combinatorial problem, we also compute, in the appendix of this paper, the asymptotic diameter of the moduli space of pants decompositions on S in the metric of elementary moves.

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Kasra Rafi. Jing Tao. "The diameter of the thick part of moduli space and simultaneous Whitehead moves." Duke Math. J. 162 (10) 1833 - 1876, 15 July 2013. https://doi.org/10.1215/00127094-2323128

Information

Published: 15 July 2013
First available in Project Euclid: 11 July 2013

zbMATH: 1277.32013
MathSciNet: MR3079261
Digital Object Identifier: 10.1215/00127094-2323128

Subjects:
Primary: 32G15
Secondary: 05C85 , 20F34

Rights: Copyright © 2013 Duke University Press

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Vol.162 • No. 10 • 15 July 2013
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