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

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- Conform. Geom. Dyn.
**4**(2000), 75-96 Request permission

## Abstract:

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.## References

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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
- 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: https://doi.org/10.1090/S1088-4173-00-00056-4
- MathSciNet review: 1755900