Paper folding, Riemann surfaces and convergence of pseudo-Anosov sequences

Autor(es)

de Carvalho, Andre ^[1] ; Hall, Toby ^[2]

Afiliação do(s) autor(es)

^[1] IME USP, Dept Matemat Aplicada, BR-05508090 Sao Paulo - Brazil

^[2] Univ Liverpool, Dept Math Sci, Liverpool L69 7ZL, Merseyside - England

• Tipo de documento: Artigo Científico
• Fonte: GEOMETRY & TOPOLOGY; v. 16, n. 4, p. 1881-1966, 2012.
• Citações Web of Science: 3

Resumo

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 Teichmuller mapping on the Riemann sphere. (AU)

• Processo FAPESP: 06/03829-2 - Dinâmica em baixas dimensões
• Beneficiário: André Salles de Carvalho
• Modalidade de apoio: Auxílio à Pesquisa - Temático