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Description
| 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 |
| Discipline: | Mathematics |
| Degree Granting Institution: | University of Illinois at Urbana-Champaign |
| Degree: | Ph.D. |
| Genre: | Dissertation |
| Subject(s): | pseudo-Anosov
dilatation 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 |
| URI: | http://hdl.handle.net/2142/16103 |
| Rights Information: | Copyright 2010 Chia-Yen Tsai |
| Date Available in IDEALS: | 2010-05-19 |
| Date Deposited: | May 2010 |
This item appears in the following Collection(s)
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Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois -
Dissertations and Theses - Mathematics