Let S be a compact Riemann surface and G a group of conformal automorphisms of S with S0 = S/G. S is a finite regular branched cover of S0. If U denotes the unit disc, let Γ and Γ0 be the Fuchsian groups with S = U/Γ and S0 = U/Γ0. There is a group homomorphism of Γ0 ontoG with kernel Γ and this is termed a surface kernel map. Two surface kernel maps are equivalent if they differ by an automorphism of Γ0. In his 1971 paper Harvey showed that when G is a cyclic group, there is a unique simplest… Expand

The concept of an adapted homology basis for a prime order conformal automorphism of a compact Riemann surface extends to arbitrary finite groups of conformal automorphisms. Here we compute some… Expand

In this paper we find a unique normal form for the symplectic matrix representation of the conjugacy class of a prime order element of the mapping-class group. We find a set of generators for the… Expand

The problem of enumeration of conjugacy classes of finite abelian sub- groups of the mapping class group Mof a compact closed surface X of genusis considered. A complete method of enumeration is… Expand

The problem of classifying all finite group actions, up to topological equivalence, on a surface of low genus is considered. Several new examples of construction and classification of actions are… Expand

The central theme of this study is Artin's braid group and the many ways that the notion of a braid has proved to be important in low-dimensional topology. In Chapter 1 the author is concerned with… Expand