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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

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A combination theorem for covering correspondences and an application to mating polynomial maps with Kleinian groups
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by Shaun Bullett PDF
Conform. Geom. Dyn. 4 (2000), 75-96 Request permission


The simplest version of the Maskit-Klein combination theorems concerns the action of a free product of two finite subgroups of $PSL(2,{\mathbb C})$ on the Riemann sphere $\hat {\mathbb C}$, when these subgroups have fundamental domains whose interiors together cover $\hat {\mathbb C}$. We prove an analogous combination theorem for covering correspondences of rational maps, making use of Douady and Hubbard’s Straightening Theorem for polynomial-like maps to describe the structure of the limit sets. We apply our theorem to construct holomorphic correspondences which are matings of polynomial maps with Hecke groups $C_p*C_q$, and we show how it may also be applied to the analysis of separable correspondences.
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Additional Information
  • Shaun Bullett
  • Affiliation: School of Mathematical Sciences, Queen Mary and Westfield College, University of London, Mile End Road, London E1 4NS, United Kingdom
  • Email:
  • Received by editor(s): September 30, 1999
  • Received by editor(s) in revised form: January 20, 2000
  • Published electronically: April 27, 2000
  • Additional Notes: I would like to thank Christopher Penrose for many helpful discussions concerning this work.
  • © Copyright 2000 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 4 (2000), 75-96
  • MSC (2000): Primary 37F05; Secondary 30D05, 30F40
  • DOI:
  • MathSciNet review: 1755900