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arXiv · 2510.04350

Quasi-geodesics in the Cannon-Thurston metric

Vaibhav Gadre·Joseph Maher·Catherine Pfaff·Caglar Uyanik
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Abstract

A closed fibered 3-manifold admits a complete hyperbolic metric if and only if it has a fibration with a pseudo-Anosov monodromy. The stable and the unstable laminations associated to the pseudo-Anosov homeomorphism on the fiber surface give rise to a natural metric on the 3-manifold, the Cannon-Thurston metric, which is quasi-isometric to the hyperbolic metric. In this paper, we describe a specific family of quasi-geodesics in the Cannon-Thurston metric. We use the main results of this article in a companion paper to obtain statistics for typical geodesics with respect to various natural measures on the 2-sphere, thus giving a geometric criterion for singularity between some of these measure classes.

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Vaibhav Gadre, Joseph Maher, Catherine Pfaff, Caglar Uyanik. 2026-07-04. Quasi-geodesics in the Cannon-Thurston metric. https://arxiv.org/abs/2510.04350

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