 
Summary: RESEARCH BLOG 5/24/04
WHAT NEXT?
At the Cornell Topology Festival, Bill Thurston gave the last talk,
entitled "What next?" He initially made some comments about his
involvement in 3manifold topology, and compared himself to Rip Van
Winkle, coming back from a mathematical hiatus to find that many
of the questions he initiated are claimed to be solved. He commented
that many ideas in 3manifold topology which seemed to lead to di
vergent areas of study have converged to form intimate relations with
each other, such as the study of various topological structures such as
laminations, contact structures, geometric structures of various types,
and gauge invariants. His main idea for what may be next is to find
more relations between these things, and to make more connections
with or applications of 3manifolds to other areas. He then mentioned
some questions which he thinks may provide fruitful areas of study.
One is the lamination of all hyperbolic 3manifolds. The set of all hy
perbolic 3manifolds forms a lamination under the GromovHausdorff
(or Chaubauty?) topology: a sequence of points converges if larger
and larger balls around the sequence converge in the GromovHausdorff
topology. He claimed that this lamination is precompact, but I don't
