On fiber-preserving isotopies of surface homeomorphisms

Abstract. We show that there are homeomorphisms of closed oriented genus g surfaces g which are ber-preserving with respect to an irregular branched covering g! S2 and isotopic to the identity, but which are not ber-isotopic to the identity. The study of branched coverings of surfaces is a classical subject which continues to play a role in modern topology, often in application to the study of manifolds of higher dimension. For instance, branched coverings of surfaces play a key role in the famous result of Hilden [5] and Montesinos [8] that every closed orientabl