Planar subdivision rules-fundamental questions
by
James Cannon
Brigham Young University

We define inversive subdivision rules, indicate how they arise in the study of 3-manifolds and Kleinian groups, and discuss some subset of the following fundamental properties of these rules: methods for finding and exhibiting explicit examples, the recursion problem, vertex behavior, characterizing mesh 0 combinatorially, replacing an inversive subdivision rule by a classical subdivision rule, direct limit tilings and expansion maps, the static and dynamic type problems, the Teichmueller problem, the geometrization problem, the tile shape problem.

Date received: April 14, 1998