On a minimal factorization conjecture

Let be a proper holomorphic map from a connected complex surface S onto the open unit disk D⊂C, with 0∈D as its unique singular value, and having fiber genus g>0 -- Assume that in case g⩾2, admits a deformation whose singular fibers are all of simple Lefschetz type -- It has been conjectured that the factorization of the monodromy f∈M around ϕ (0) in terms of righ-thanded Dehn twists induced by the monodromy of has the least number of factors among all possible factorizations of f as a product of righthanded Dehn twists in the mapping class group (see [M. Ishizaka, One parameter families of Riemann surfaces and presentations of elements of mapping class group by Dehn twists, J. Math. Soc. Japan 58 (2) (2006) 585–594]) -- In this article, the validity of this conjecture is established for g=1

• Autores: Cadavid, Carlos A.; Vélez, Juan D.
• Fecha de publicación: 2007
• Institución: Universidad EAFIT
• Repositorio: Repositorio EAFIT
• Idioma: eng
• OAI Identifier: oai:repository.eafit.edu.co:10784/9780
• Acceso en línea: http://hdl.handle.net/10784/9780
• Palabra clave: SUPERFICIES DE RIEMANN; TOPOLOGÍA ALGEBRÁICA; GEOMETRÍA DIFERENCIAL; ANÁLISIS MATEMÁTICO; ISOMORFISMO (MATEMÁTICAS); Riemann surfaces; Algebraic topology; Geometry, differential; Mathematical analysis; Isomorphisms (Mathematics); Riemann surfaces; Algebraic topology; Geometry; differential; Mathematical analysis; Isomorphisms (Mathematics); Fibraciones elípticas; Monodromía
• License: Acceso abierto