• Corpus ID: 233481982

Extending Harvey's Surface Kernel Maps

  title={Extending Harvey's Surface Kernel Maps},
  author={Jane Gilman},
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… 


Introduction to Riemann Surfaces Chelsea Publishing Co., 2nd edition
  • Mathematics & CS department,
  • 1957
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A Matrix Representation for Automorphisms of Riemann Surfaces
  • Linear Algebra and its Applications
  • 1977
A Matrix Representation for Automorphisms of Riemann Surfaces, Linear Algebra and its Applications
  • 1977
Braids, Links, and Mapping Class Groups.
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
Links and Mapping Class Groups
  • Anals of Math. Studies
  • 1974