Geodesic
Mating quadratic maps with Kleinian groups via quasiconformal surgery
Bullett, S.1 ; Harvey, W.2
1 School of Mathematical Sciences, Queen Mary and Westfield College, University of London, Mile End Road, London E1 4NS, United Kingdom
2 Department of Mathematics, King’s College, University of London, Strand, London WC2R 2LS, United Kingdom
Electronic research announcements of the American Mathematical Society, Tome 06 (2000), pp. 21-30 Cet article a éte moissonné depuis la source American Mathematical Society

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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 $p(z,w)=0$.
DOI : 10.1090/S1079-6762-00-00076-7

Bullett, S. 1 ; Harvey, W. 2

1 School of Mathematical Sciences, Queen Mary and Westfield College, University of London, Mile End Road, London E1 4NS, United Kingdom
2 Department of Mathematics, King’s College, University of London, Strand, London WC2R 2LS, United Kingdom 
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Bullett, S.; Harvey, W. Mating quadratic maps with Kleinian groups via quasiconformal surgery. Electronic research announcements of the American Mathematical Society, Tome 06 (2000), pp. 21-30. doi: 10.1090/S1079-6762-00-00076-7

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