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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