 
Summary: RESEARCH BLOG 8/03/04
Last week, I. Kapovich and Weidmann posted a paper showing that
there is an algorithm to solve the rank problem for torsion free, convex
cocompact Kleinian groups. I haven't read enough of their paper to
understand how it goes, but from what I can gather, they use gener
alizations of Nielsen techniques to actions on wordhyperbolic spaces,
which they have developed in previous papers. They also make use
of tameness of subgroups. It would be interesting to generalize their
result to show that there is an algorithm to compute the rank for all
fundamental groups of (good) compact 3orbifolds.
Boileau and Weidmann have a paper which gives a structure theorem
for 3manifolds with nontrivial JSJ decomposition and which have two
generated fundamental group. They would like to rule out one case,
which comes down to showing that a 2bridge link cannot be an irregu
lar cover of a manifold with a single boundary torus. I believe it should
be possible to show this using the techniques I've developed for classi
fying 2parabolic generator groups. In fact, I think one should be able
to classify the commensurators of (nonarithmetic) 2bridge links, and
then show that there is no manifold cover between a 2bridge link and
the minimal orbifold which it covers (one may deal with the arithmetic
