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Paper folding, Riemann
surfaces and convergence of pseudo-Anosov sequences
André de Carvalho and Toby Hall |
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Geometry & Topology 16 (2012) 1881–1966
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Abstract |
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A method is presented for constructing closed surfaces out of Euclidean polygons with infinitely many segment identifications along the boundary. The metric on the quotient is identified. A sufficient condition is presented which guarantees that the Euclidean structure on the polygons induces a unique conformal structure on the quotient surface, making it into a closed Riemann surface. In this case, a modulus of continuity for uniformising coordinates is found which depends only on the geometry of the polygons and on the identifications. An application is presented in which a uniform modulus of continuity is obtained for a family of pseudo-Anosov homeomorphisms, making it possible to prove that they converge to a Teichmüller mapping on the Riemann sphere. |
Keywords
geometric structures on surfaces, Riemann surfaces,
pseudo-Anosov sequences
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Mathematical Subject Classification 2010
Primary: 30C35, 30F10, 37E30
Secondary: 30C62, 30F45, 37F30
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References |
Publication
Received: 18 July 2011
Revised: 5 April 2012
Accepted: 30 May 2012
Published: 27 August 2012
Proposed: Danny Calegari
Seconded: Leonid Polterovich, Yasha Eliashberg
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Authors |
| André de Carvalho | |
| Departamento de Matemática Aplicada,
IME - USP Rua do Matão 1010 Cidade Universitária 05508-090 São Paulo Brazil |
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| Toby Hall | |
| Department of Mathematical
Sciences University of Liverpool Liverpool L69 7ZL UK |
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