A combination theorem for covering correspondences and an application to mating polynomial maps with Kleinian groups

Author:
Shaun Bullett

Journal:
Conform. Geom. Dyn. **4** (2000), 75-96

MSC (2000):
Primary 37F05; Secondary 30D05, 30F40

Published electronically:
April 27, 2000

MathSciNet review:
1755900

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Abstract | References | Similar Articles | Additional Information

The simplest version of the Maskit-Klein combination theorems concerns the action of a free product of two finite subgroups of on the Riemann sphere , when these subgroups have fundamental domains whose interiors together cover . 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 , 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:
s.r.bullett@qmw.ac.uk

DOI:
https://doi.org/10.1090/S1088-4173-00-00056-4

Keywords:
Holomorphic dynamics,
polynomial maps,
Kleinian groups

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.

Article copyright:
© Copyright 2000
American Mathematical Society