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
DOI:
https://doi.org/10.1090/S1079-6762-00-00076-7
Published electronically:
March 28, 2000
MathSciNet review:
1751536
Full-text PDF Free Access
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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
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
