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Title:Curves on surfaces
Author(s):Maungchang, Rasimate
Director of Research:Leininger, Christopher J.
Doctoral Committee Chair(s):Dunfield, Nathan M.
Doctoral Committee Member(s):Leininger, Christopher J.; Kapovitch, Ilia; Athreya, Jayadev S.
Department / Program:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Sunada construction
Length spectral
finite rigidity
pants graphs
Abstract:This dissertation is concerned with geometric and combinatoric problems of curves on surfaces. In Chapter 3, we show that certain families of iso-length spectral hyperbolic surfaces obtained via the Sunada construction are not generally simple iso-length spectral. In Chapter 4, We prove a strong form of finite rigidity for pants graphs of spheres. Specifically, for any n ≥ 5 we construct a finite subgraph Xn of the pants graph P(S0,n) of the n-punctures sphere S0,n with the following property. Any simplicial embedding of Xn into any pants graph P(S0,m) of a punctured sphere is induced by an embedding S0,n → S0,m.
Issue Date:2013-05-24
Rights Information:Copyright 2013 by Rasimate Maungchang. All rights reserved.
Date Available in IDEALS:2013-05-24
Date Deposited:2013-05

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