University of Illinois Urbana-Champaign

Curves on surfaces

Maungchang, Rasimate

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https://hdl.handle.net/2142/44347

Description

Title
Curves on surfaces
Author(s)
Maungchang, Rasimate
Issue Date
2013-05-24T22:08:32Z
Director of Research (if dissertation) or Advisor (if thesis)
Leininger, Christopher J.
Doctoral Committee Chair(s)
Dunfield, Nathan M.
Committee Member(s)
  • Leininger, Christopher J.
  • Kapovitch, Ilia
  • Athreya, Jayadev S.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(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.
Graduation Semester
2013-05
Permalink
http://hdl.handle.net/2142/44347
Copyright and License Information
Copyright 2013 by Rasimate Maungchang. All rights reserved.

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