Quasi-Fuchsian correspondences.
Abstract
We consider the action of holomorphic correspondences or equally algebraic
functions acting on the Riemann sphere C and their limit sets: a holomorphic
correspondence is a polynomial relation, P(z;w) = 0 in z and w: A holomorphic
correspondence P(z;w) = 0 is said to be an (n : m) correspondence if
the degrees of z and w in P are n and m respectively.
We identify a class of (2 : 2) holomorphic correspondences whose limit
set is a topological circle where on a component of the complement of the
limit set, the action of the correspondence is conjugate to the action of the
Modular group PSL(2; Z) on the upper half plane.
Further, we generalise these results to a class of (3 : 3) holomorphic
correspondences with analogous properties.
Authors
Samarasinghe, Manjula LCollections
- Theses [3834]