Dave Futer’s talk at Brown

On November 30, Dave Futer is speaking in the Geometry-Topology seminar at Brown University. He will speak about:

Title: Cusp geometry of fibered 3-manifolds

Abstract: Let F be a surface with punctures, and suppose that \varphi: F  \to F is a pseudo-Anosov homeomorphism fixing a puncture p of F. Then the mapping torus of \varphi is a hyperbolic 3-manifold M_\varphi, which contains a maximal cusp C corresponding to the puncture p. We show that the geometry of the maximal cusp C can be predicted, up to explicit multiplicative error, by the action of \varphi on the complex of essential arcs of in the surface F, denoted A(F).

This result is motivated by an analogous theorem of Brock, which predicts the volume of M_\phi in terms of the action of \varphi on the pants graph P(F). However, in contrast with Brock’s theorem. our result gives effective estimates, and is proved using completely elementary methods. This is joint work with Saul Schleimer.

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