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ISSN 1079-6762

Mating quadratic maps with Kleinian groups via quasiconformal surgery


Authors: S. R. Bullett and W. J. Harvey
Journal: Electron. Res. Announc. Amer. Math. Soc. 6 (2000), 21-30
MSC (2000): Primary 37F05; Secondary 30D05, 30F40, 37F30
Published electronically: March 28, 2000
MathSciNet review: 1751536
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Abstract:

Let $q:\hat{\mathbb C} \to \hat{\mathbb C}$ be any quadratic polynomial and $r:C_2*C_3 \to PSL(2,{\mathbb C})$ be any faithful discrete representation of the free product of finite cyclic groups $C_2$ and $C_3$ (of orders $2$ and $3$) having connected regular set. We show how the actions of $q$ and $r$ can be combined, using quasiconformal surgery, to construct a $2:2$holomorphic correspondence $z \to w$, defined by an algebraic relation $p(z,w)=0$.


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Additional Information

S. R. 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

W. J. Harvey
Affiliation: Department of Mathematics, King’s College, University of London, Strand, London WC2R 2LS, United Kingdom
Email: bill.harvey@kcl.ac.uk

DOI: http://dx.doi.org/10.1090/S1079-6762-00-00076-7
PII: S 1079-6762(00)00076-7
Keywords: Holomorphic dynamics, quadratic maps, Kleinian groups, quasiconformal surgery, holomorphic correspondences
Received by editor(s): December 22, 1999
Published electronically: March 28, 2000
Communicated by: Svetlana Katok
Article copyright: © Copyright 2000 American Mathematical Society