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Wednesday, May 3, 2017

Doob Colloquium
3:00 pm   in 243 Altgeld Hall,  Wednesday, May 3, 2017
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Submitted by icontrer.
Rosemary Guzman (UIUC)
Quantitative Mostow Rigidity: Relating volume to topology for hyperbolic 3-manifolds
Abstract: A celebrated result of Mostow states that if M, N are two closed, con- nected, orientable, hyperbolic n-manifolds which are homotopy equivalent in dimensions $n\geq 3$, then M, N are equivalent up to isometry. This unique geometric-topological relationship has been the framework for many important results in the field, including notable results providing lower bounds on the volume of M, and results relating volume to homology (Culler-Shalen). In this talk, we will focus on the case where the fundamental group of M has a property, $k-$free, for $k\geq5$, and discuss current work toward an improvement on the volume bound from the current known bound of 3.44 which holds for $k\geq 4$. This is joint work with Peter Shalen.