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Measured laminations, train tracks, and geodesic planes

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Yongquan Zhang
Don, 16/12/2021 - 15:00 - 16:00
Parent event: 

Zoom only.
Meeting ID: 931 7291 0947
For passcode please contact Christian Kaiser (

Given a measured geodesic lamination L on a hyperbolic surface, does there exist an infinite geodesic ray with finite transverse measure with resepct to L? Geodesic rays eventually disjoint from L or asymptotic to a leaf of L are obvious candidates, but are there others? In this talk, I will discuss joint work with Tina Torkaman which shows that the answer to the question above is always yes, provided that L is not a multicurve. The proof is based on a symbolic coding scheme coming from a squence of train tracks that carry L. As an application, I will relate the existence of such geodesic rays to the existence of certain geodesic planes in a quasifuchsian manifold, which are disjoint from the convex core, limiting on the convex core, but cannot be separated from the core by a supporting plane of the convex core boundary.

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