Mating quadratic maps with Kleinian groups via quasiconformal surgery

Let q : (C) over cap --> (C) over cap be any quadratic polynomial and r : C -2 * C-3 --> PSL(2, 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 conn ected regular set. We show how the actions of q and r can be combined, usin g quasiconformal surgery, to construct a 2 : 2 holomorphic correspondence z --> w, defined by an algebraic relation p(z; w) = 0.