UBC Mathematics Colloquium

Juan Souto
(University of Michigan)


Relations between geometry and topology of hyperbolic 3-manifolds

Wed., Dec. 9, 2009, 3:00pm, MATX 1100


By Mostow's rigidity theorem, geometric invariants of
hyperbolic 3-manifolds are in fact topological invariants. On the
other hand, it follows from the work of Thurston and Perelman that a
3-manifold is hyperbolic if and only if it satisfies some rather mild
conditions. In light of these results, it is an interesting
question to try to understand how topological conditions on a
3-manifold $M$ which admits a hyperbolic metric affect the geometry of
the hyperbolic metric. This question is rather imprecise. In other
words, it has many different incarnations. In this talk I will
describe a few results on different concrete formulations of the
question above.

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