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| Author(s): |
Eduardo Carvalho Bento Gonçalves
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica |
| Defense date: | 2010-01-07 |
| Examining board members: |
Alexandre Ananin;
Alcibiades Rigas;
Misha Verbitsky
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| Advisor: | Alexandre Ananin |
| Abstract | |
First, we present an introduction to plane hyperbolic geometry, which may be useful even for a beginner. Next, using the concept of "simple earthquake", we explicitly describe, in terms of some natural coordinates, the Teichmüller space T Hn of hyperelliptic surfaces. This description turns out to be simple: T Hn is the space of certain (2n ? 6)-tuples of points in the ideal boundary of the hyperbolic plane. Based on the description in question, many results are presented, including: a simple and effective criterion which allows one to verify if a given representation of a surface group in the group of isometries of the hyperbolic plane is faithful and discrete; a new and elementary proof for a result of W. Goldman, which characterizes the faithful and discrete representations as being those which have maximal Toledo invariant; a new and elementary proof for a theorem of D. Toledo, relative to the rigidity of representations of surface groups in the group of holomorphic isometries of the complex hyperbolic space. key-words: Area, discreteness, representations, plane hyperbolic geometry, Teichmüller space, complex hyperbolic geometry (AU) | |
| FAPESP's process: | 07/56989-0 - Fibrados hiperelipticos em geometrias classicas. |
| Grantee: | Eduardo Carvalho Bento Gonçalves |
| Support Opportunities: | Scholarships in Brazil - Master |