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RESEARCH BLOG 8/18/03 I spent two weeks in Cambridge at the Isaac Newton Institute at
 

Summary: RESEARCH BLOG 8/18/03
I spent two weeks in Cambridge at the Isaac Newton Institute at
the program on Spaces of Kleinian groups and Hyperbolic 3-manifolds.
Notes from the talks will eventually be available at the web site, I'll
mention in this blog when this occurs.
One of the main goals of the field of Kleinian groups is to give a com-
plete classification of them. Another major goal is to understand qual-
itative and quantitative geometric and dynamical information about
Kleinian groups. There has been much progress on these questions,
and the conference had many of the experts there (some people were
missing for personal reasons, such as Jeff Brock who just had a new
baby). Thurston proposed a classification of Kleinian groups called
the ending lamination conjecture, which gives a parameterization in
terms of the structure of the hyperbolic manifold at infinity. Brock,
Canary, and Minsky announced the proof of this conjecture for the
class of tame hyperbolic manifolds, completing a program which Min-
sky has developed over many years (and depending on work of many
others, especially Masur). The question of whether hyperbolic mani-
folds with finitely generated fundamental groups are tame is known as
the Marden conjecture, and seems to be the main obstruction to the

  

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

 

Collections: Mathematics