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Doctoral Thesis
Full name
Minoru Enrique Akiyama Figueroa
Knowledge Area
Date of Defense
São Paulo, 2018
Carvalho, André Salles de (President)
Bertolini, Marcel Vinhas
Bonnot, Sylvain Philippe Pierre
Nitecki, Zbigniew Henry
Zanata, Salvador Addas
Title in Portuguese
Estimativas das coordenadas de comprimento para um espaço de papel furado
Keywords in Portuguese
Espaços de papel
Pontos cônicos
Pontos irregulares
Superfícies gaita de fole
Abstract in Portuguese
Espaços de papel são quocientes métricos obtidos ao identificar num multipolígono P C, pares de subsegmentos do bordo de P por isometrías que revertem orientação. Tais espaços aparecem por exemplo em [dC05], onde mostra-se uma receita para construir, a partir de certos homeomorfismos definidos numa superfície compacta, um homeomorfismo chamado de pseudo-Anosov generalizado (pois generalizam os pseudo-Anosov clássicos definidos por Thurston), o qual está definido sobre um espaço de papel homeomorfo à superfície original. Por outro lado, um espaço de papel S tem uma estrutura complexa natural em todos seus pontos exceto, possívelmente, num conjunto fechado Q S de pontos chamados irregulares. Neste trabalho será considerado a superfície hiperbólica S obtida a partir de uma esfera de papel S com m pontos irregulares, ao tirar dela seu conjunto de pontos irregulares junto com os pontos com curvatura positiva. Na esfera de papel furada S será descrita uma família de curvas geodésicas que descompõem à S em calças e serão calculados estimativas para os comprimentos hiperbólicos dessas curvas.
Title in English
Estimates of the length coordinates for a punctured paper space
Keywords in English
Bagpipes surfaces
Conics points
Irregular points
Paper spaces
Abstract in English
Paper spaces are metric quotients obtained by identifying, given a multipolygon P C, pairs of subsegments of the edge of P by orientation reversing isometries. Such spaces appear for example in [dC05], where a recipe is given to construct, starting from certain homeomorphism on a compact surface, an homeomorphism called generalized pseudo-Anosov map (as these generalize the classical pseudo-Anosov defined by Thurston), which is defined on a paper space homeomorphic to the original surface. On the other hand a paper space S has a natural complex structure at each of its points except, possibly, on a closed set Q S of points called irregular. In this work will be considerer the hyperbolic surface S obtained, from a paper sphere S with m irregularities, by taking from it the set of irregular points together with the positive curvature points. On the punctured paper sphere S will be described a family of geodesic curves which decompose S into pairs of pants and will be also calculated stimates for the hyperbolic lengths of those curves.
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