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Title:Minimal pseudo-Anosov translation lengths on the Teichmuller space
Author(s):Tsai, Chia-Yen
Director of Research:Leininger, Christopher J.
Doctoral Committee Chair(s):Kapovitch, Ilia
Doctoral Committee Member(s):Leininger, Christopher J.; Bradlow, Steven B.; Dunfield, Nathan M.
Department / Program:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
mapping class group
Teichmuller space
Abstract:This thesis is a study of the asymptotic behavior of minimal pseudo-Anosov translation lengths on the Teichmuller space. For tori with n marked points, we find an upper bound for the minimal pseudo-Anosov translation length. The upper bound is on the order of 1/|χ(S)| . We find similar asymptotics for genus g surfaces with n marked points as g and n vary in certain prescribed ways. However, for a surface S with fixed genus g ≥ 2 and varied n, we prove that the asymptotic behavior (in n) is different. The main result of this thesis is that the least pseudo-Anosov translation length shrinks to zero on the order of log |χ(S)|/|χ(S)| as |χ(S)| → ∞. This is in contrast with the previously-known results for the cases of closed surfaces and marked spheres, in which the behavior is on the order of 1/|χ(S)| . These results are published in [Tsa09].
Issue Date:2010-05-19
Rights Information:Copyright 2010 Chia-Yen Tsai
Date Available in IDEALS:2010-05-19
Date Deposited:May 2010

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