2016-11-302007-080166-8641http://hdl.handle.net/10784/9780Let 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=1application/pdfenginfo:eu-repo/semantics/openAccessinfo:eu-repo/semantics/articleSUPERFICIES DE RIEMANNTOPOLOGÍA ALGEBRÁICAGEOMETRÍA DIFERENCIALANÁLISIS MATEMÁTICOISOMORFISMO (MATEMÁTICAS)Riemann surfacesAlgebraic topologyGeometry, differentialMathematical analysisIsomorphisms (Mathematics)Riemann surfacesAlgebraic topologyGeometrydifferentialMathematical analysisIsomorphisms (Mathematics)Fibraciones elípticasMonodromíaAcceso abierto2016-11-30Cadavid, Carlos A.Vélez, Juan D.10.1016/j.topol.2007.06.003