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. Lower postnikov terms of generalized CW complexes and semi-simple actions....Pages 1-23 3-fold branched coverings and the mapping class group of a surface....Pages 24-46 Locally flat embeddings of three dimensional manifolds in four dimensional manifolds....Pages 47-49 Differential characters and geometric invariants....Pages 50-80 Minimal branched immersions into three-manifolds....Pages 81-94 Representations of fundamental groups of surfaces....Pages 95-117 Comparison theorems for volumes in surfaces....Pages 118-124 The isometry-invariant geodesics problem: Closed and open....Pages 125-140 Attractors for discrete-time monotone dynamical systems in strongly ordered spaces....Pages 141-153 Presentation classes, 3-manifolds and free products....Pages 154-167 Proper actions on homogeneous spaces....Pages 168-179 Deformation spaces for seifert manifolds....Pages 180-216 Abelian invariants of satellite knots....Pages 217-227 An introduction to compactifying spaces of hyperbolic structures by actions on trees....Pages 228-240 A note on an invariant of fintushel and stern....Pages 241-244 Handlebodies and 2-complexes....Pages 245-259 Extrema associated with homotopy classes of maps....Pages 260-267 Geometries and geometric structures in real dimension 4 and complex dimension 2....Pages 268-292