Topological Classification of Conformal Actions on pq-Hyperelliptic Riemann Surfaces

Research Article Topological Classification of Conformal Actions on pq-Hyperelliptic Riemann Surfaces

0 Se p 20 07 Exceptional Points in the Elliptic - Hyperelliptic Locus

An exceptional point in the moduli space of compact Riemann surfaces is a unique surface class whose full automorphism group acts with a triangular signature. A surface admitting a conformal involution with quotient an elliptic curve is called elliptic-hyperelliptic; one admitting an anticonformal involution is called symmetric. In this paper, we determine, up to topological conjugacy, the full...

The Geometry of Two Generator Groups: Hyperelliptic Handlebodies

A Kleinian group naturally stabilizes certain subdomains and closed subsets of the closure of hyperbolic three space and yields a number of different quotient surfaces and manifolds. Some of these quotients have conformal structures and others hyperbolic structures. For two generator free Fuchsian groups, the quotient three manifold is a genus two solid handlebody and its boundary is a hyperell...

On p-hyperelliptic Involutions of Riemann Surfaces

A compact Riemann surface X of genus g > 1 is said to be phyperelliptic if X admits a conformal involution ρ, called a p-hyperelliptic involution, for which X/ρ is an orbifold of genus p. Here we give a new proof of the well known fact that for g > 4p + 1, ρ is unique and central in the group of all automorphisms of X. Moreover we prove that every two p-hyperelliptic involutions commute for 3p ...

Correlation Functions for Some Conformal Theories on Riemann Surfaces

We discuss the geometrical connection between 2D conformal field theories, random walks on hyperbolic Riemann surfaces and knot theory. For the wide class of CFT’s with monodromies being the discrete subgroups of SL(2,R I ) the determination of four–point correlation functions are related to construction of topological invariants for random walks on multipunctured Riemann surfaces.