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Master's Dissertation
DOI
10.11606/D.45.2015.tde-27082015-073617
Document
Author
Full name
Angélica Turaça
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2015
Supervisor
Committee
Carvalho, André Salles de (President)
Boyland, Philip Lewis
Tal, Fabio Armando
Title in Portuguese
As coordenadas de Fenchel-Nielsen
Keywords in Portuguese
Coordenadas de Fenchel-Nielsen.
Espaço de Teichmüller
Geometria hiperbólica
Superfície de Riemann
Abstract in Portuguese
Nesta dissertação, definimos a geometria hiperbólica usando o disco de Poincaré (D2) e o semiplano superior (H2) com as respectivas propriedades. Além disso, apresentamos algumas funções e relações importantes da geometria hiperbólica; conceituamos as superfícies de Riemann, analisando suas propriedades e representações; estudamos o espaço de Teichmüller com a devida decomposição em calças. Esses temas são ferramentas necessárias para atingir o objetivo da dissertação: definir as coordenadas de Fenchel Nielsen como um sistema de coordenadas locais do espaço de Teichmüller Tg.
Title in English
Fenchel-Nielsen Coordinate
Keywords in English
Fenchel-Nielsen coordinate.
Hyperbolic geometry
Riemann surface
Teichmüller space
Abstract in English
In this dissertation, we defined the hyperbolic geometry using the Poincares disk (D2) and upper half-plane (H2) with its properties. Besides, we presented some functions and important relations of the hyperbolic geometry; we conceptualize the Riemann surfaces, analyzing its properties and representations; we studied the Teichmüller Space with proper decomposition pants. These themes are essential tools to reach the goal of the work: The definition of the Fenchel Nielsen coordenates as local coordinate system of the Teichmüller space Tg.
 
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Fenchel_Nielsen.pdf (1.04 Mbytes)
Publishing Date
2015-08-27
 
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