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
Date of Ingest
2013-05-24T22:08:32Z
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
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