Curves on surfaces

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2013

Author dc:creator

• Maungchang, Rasimate

Contributors dc:contributor

• Leininger, Christopher J.
• Dunfield, Nathan M.
• Kapovitch, Ilia
• Athreya, Jayadev S.

• Sunada construction
• Length spectral
• finite rigidity
• pants graphs

Statement dc:rights

• Copyright 2013 by Rasimate Maungchang. All rights reserved.

Language dc:language

en

Handle dc:identifier

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

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/44347