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Conformal Geometry and Dynamics

ISSN 1088-4173



Pinching holomorphic correspondences

Authors: Shaun Bullett and Peter Haïssinsky
Journal: Conform. Geom. Dyn. 11 (2007), 65-89
MSC (2000): Primary 37F05; Secondary 37F30
Published electronically: June 5, 2007
MathSciNet review: 2314243
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Abstract: 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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Additional Information

Shaun Bullett
Affiliation: School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, United Kingdom

Peter Haïssinsky
Affiliation: LATP/CMI, Université de Provence, 39 rue Frédéric Joliot-Curie, 13453 Marseille Cedex 13, France

Keywords: Holomorphic correspondences, matings, quasiconformal deformations, pinching, circle-packing
Received by editor(s): June 19, 2006
Published electronically: June 5, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.