Geometry And Topology: Proceedings Of The Special Year Held At The University Of Maryland, College Park, 1983 - 1984 (lecture Notes In Mathematics)

Let p :F ÷ D be a simple 3-sheeted branched covering of a 2disc D, with an even number of branch values. Let L be the group of isotopy classes of liftable orientation-preserving homeomorphisms of D rel ~D. Then lifting induces a homomorphism 1 from L to the mapping class group of F. In this paper we prove that 1 is surjective, and find a simple set of generators for L and two elements of L whose normal closure in L is kernel I. Thus the mapping class group of F is exhibited as a quotient group of the group L, which is a subgroup of finite index in Artin's braid group. i.