Cannon's conjecture, finite subdivision rules, and rational maps
William Floyd

In these two talks we give an overview of the approach to Cannon's conjecture taken by Cannon, Floyd, Parry and others. Cannon's Combinatorial Riemann Mapping Theorem gives an approach to the conjecture via the action of the group on its space at infinity. Finite subdivision rules give a model for the recursion at infinity. They can also be used to model critically finite branched maps acting on the 2-sphere.



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