# 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

Abstract:

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.