 
Summary: RESEARCH BLOG 3/27/04, STDC '04
I went to two days of the Spring Topology and Dynamics Conference,
held at University of Alabama at Birmingham. Jim Cannon started off
with a talk on subdivision tilings for hyperbolic groups. For a long
time, he and Floyd and Parry have been working on the conjecture
that irreducible closed 3manifolds with infinite wordhyperbolic fun
damental group are actually hyperbolic. This would be one step in an
approach to the geometrization conjecture, which I think would still
be quite interesting program to carry through, even if Perelman's ar
guments using Ricci flow are correct.
Cannon discussed joint work with Floyd, Hersonsky, and Parry, in
which they show that to a hyperbolic group , one may associate a
subdivision tiling which in some sense recursively constructs . The
main example of such subdivision tilings known before was for compact
NPC cubed spaces. In Cannon's classic paper [1], he shows that for
a hyperbolic manifold, there are only finitely many "cone types". A
cone type is a subset of the Cayley graph with respect to a fixed set
of generators, which (roughly) is the set of all geodesics which have a
common prefix (up to equivalence by truncating prefixes). Cannon's
argument generalizes directly to hyperbolic groups. Take the ball of
