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Geometry-Topology Seminar

Tuesday, April 17, 2018 - 4:30pm

David Futer

Temple University


University of Pennsylvania

DRL 4N30

This is a continuation of the Geometry-Topology "Show-and-Tell" Seminar

The study of hyperbolic manifolds often begins with the thick-thin decomposition. Given a number epsilon > 0, we decompose a manifold into the epsilon-thin part (points on essential loops of length less than epsilon), and the epsilon-thick part (everything else). The Margulis lemma says that there is a universal number epsilon_n, depending only on the dimension (and nothing else!), such that the thin part of every hyperbolic n-manifold has very simple topology.

In dimension 3, we still do not know the optimal Margulis constant epsilon_3. Part of the problem is that while the topology is simple, the geometry of epsilon-thin tubes can be quite complicated. I will describe some joint work in progress with Jessica Purcell and Saul Schleimer, which can help give quantitative control on the Margulis constant.