Outdated Archival Version

These pages are not updated anymore. They reflect the state of 20 August 2005. For the current production of this journal, please refer to http://www.math.psu.edu/era/.

This journal is archived by the American Mathematical Society. The master copy is available at http://www.ams.org/era/

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 $p(z,w)=0$.

Copyright 2000 American Mathematical Society

TeX source (32.4K)
DVI (44K)
PostScript (215.1K)

Article Info

• ERA Amer. Math. Soc. 06 (2000), pp. 21-30
• Publisher Identifier: S 1079-6762(00)00076-7
• 2000 Mathematics Subject Classification. Primary 37F05; Secondary 30D05, 30F40, 37F30
• Key words and phrases. Holomorphic dynamics, quadratic maps, Kleinian groups, quasiconformal surgery, holomorphic correspondences
• Received by the editors December 22, 1999
• Posted on March 28, 2000
• Communicated by Svetlana Katok
• Comments (When Available)

S. R. Bullett

School of Mathematical Sciences, Queen Mary and Westfield College, University of London, Mile End Road, London E1 4NS, United Kingdom

E-mail address: s.r.bullett@qmw.ac.uk

W. J. Harvey

Department of Mathematics, King's College, University of London, Strand, London WC2R 2LS, United Kingdom

E-mail address: bill.harvey@kcl.ac.uk