Minimal pseudo-Anosov translation lengths on the Teichmuller space

pseudo-Anosov;dilatation;mapping class group;Teichmuller space

Tsai, Chia-Yen

关键词: pseudo-Anosov;    dilatation;    mapping class group;    Teichmuller space;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/16103/Tsai_Chia-Yen.pdf?sequence=2&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

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-Anosovtranslation 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].