Summary: RESEARCH BLOG 3/07/03
This week there were two talks at U. of C. on hyperbolic 3-manifolds.
Juan Souto is visiting Jeff Brock and Chris Connell, so Peter Storm,
a student of Dick Canary, came to visit as well. Pete will be at U. of
Chicago next year on an NSF postdoc.
Juan Souto gave a talk on Thursday, on the Marden conjecture. My
advisor, Mike Freedman, spent many years working on this conjecture.
Marden didn't actually state it as a conjecture, but as a question . It
seems to be the last major step in obtaining a complete classification of
Kleinian groups, with the solution of the ending lamination conjecture
by Brock, Canary, and Minsky . The Marden conjecture states that
every hyperbolic 3-manifold with finitely generated fundamental group
is topologically tame. By work of Bonahon, this is known in the case
that the fundamental group is freely indecomposable. Souto proves this
in the case that the manifold may be exhausted by compact cores, that
is compact submanifolds which are homotopy equivalent to the mani-
fold. Souto uses a trick of Canary, by taking a homologically trivial loop
in the "Masur domain", and taking the two-fold branched cover to get
a manifold with irreducible fundamental group and a negatively curved
metric. Now, the lifts of boundaries of the compact cores disjoint from