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RESEARCH BLOG 5/24/04 At the Cornell Topology Festival, Bill Thurston gave the last talk,

Summary: RESEARCH BLOG 5/24/04
At the Cornell Topology Festival, Bill Thurston gave the last talk,
entitled "What next?" He initially made some comments about his
involvement in 3-manifold 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 3-manifold 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 3-manifolds to other areas. He then mentioned
some questions which he thinks may provide fruitful areas of study.
One is the lamination of all hyperbolic 3-manifolds. The set of all hy-
perbolic 3-manifolds forms a lamination under the Gromov-Hausdorff
(or Chaubauty?) topology: a sequence of points converges if larger
and larger balls around the sequence converge in the Gromov-Hausdorff
topology. He claimed that this lamination is precompact, but I don't


Source: Agol, Ian - Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago


Collections: Mathematics