This Friday, March 30, Dave Futer is speaking in the special session on Geometric Topology and Group Theory at the AMS Central Section Meeting in Lawrence, KS.
Title: Cusp geometry of fibered 3-manifolds
Abstract: Let 
be a surface with punctures, and suppose that 
is a pseudo-Anosov homeomorphism fixing a puncture 
of . Then the mapping torus of 
is a hyperbolic 3-manifold 
, which contains a maximal cusp 
corresponding to the puncture . We show that the geometry of the maximal cusp can be predicted, up to explicit multiplicative error, by the action of on the complex of essential arcs of in the surface , denoted 
.
This result is motivated by an analogous theorem of Brock, which predicts the volume of 
in terms of the action of on the pants graph 
. 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.
Like this:
Like Loading...
