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Article Dans Une Revue Conformal Geometry and Dynamics Année : 2007

Pinching Holomorphic Correspondences

Peter Haïssinsky

Résumé

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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Dates et versions

hal-00004595 , version 1 (30-03-2005)

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Shaun Bullett, Peter Haïssinsky. Pinching Holomorphic Correspondences. Conformal Geometry and Dynamics, 2007, 11, pp.65-89. ⟨hal-00004595⟩
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