Linear progress in fibres

Vaibhav Gadre (University of Glasgow)

Monday 29th November, 2021 16:00-17:00 Online


Thurston proved that a fibred 3-manifold is hyperbolic if and only if it admits a pseudo-Anosov monodromy. From the perpsective of the universal covers, the fibration induces a map from the hyperbolic plane (as the universal cover of the fibre) to the hyperbolic 3-space (as the universal cover of the 3-manifold) that is exponentially distorted for the respective metrics, that is, there are segments in the hyperbolic plane whose endpoints when mapped into hyperbolic 3-space are logarithmic distance apart. Here, we show that a typical ray in the hyperbolic plane is on average undistorted, that is, it makes linear progress in the ambient metric on hyperbolic 3-space. 

We show that the result also holds for analogous surface/ surface group extensions. 
This is joint work with Sebastian Hensel.

The talk will be preceded by a tea time at 3:45pm. The Zoom link for the seminar is and the passcode is the genus of the two-dimensional sphere (4 letters, all lowercase).

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