Pinching Holomorphic Correspondences

Details Pinching Holomorphic Correspondences Pinching Holomorphic Correspondences

2005-03-30

arxiv.org/abs/math/0503706v1

Conformal Geometry and Dynamics 11 (05/06/2007) 65-89

Mathematics

Dynamical Systems

Scientific paper

For certain classes of holomorphic correspondences which are matings between Kleinian groups and polynomials, we prove the existence of pinching deformations, analogous to Maskit's deformations of Kleinian groups which pinch loxodromic elements to parabolic elements. We apply our results to establish the existence of matings between quadratic maps and the modular group, for a large class of quadratic maps, and of matings between the quadratic map $z\to z^2$ and circle-packing representations of the free product $C\_2*C\_3$ of cyclic groups of order 2 and 3.

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