The metric space of geodesic laminations on a surface II: small surfaces
Francis Bonahon, Xiaodong Zhu
Abstract
We continue our investigation of the space of geodesic laminations on a surface, endowed with the Hausdorff topology. We determine the topology of this space for the once-punctured torus and the 4-times-punctured sphere. For these two surfaces, we also compute the Hausdorff dimension of the space of geodesic laminations, when it is endowed with the natural metric which, for small distances, is -1 over the logarithm of the Hausdorff metric. The key ingredient is an estimate of the Hausdorff metric between two simple closed geodesics in terms of their respective slopes.
Create a lesson
Related papers
Using Transformers to Generate 3-Manifold Triangulations
Daniel Bruwel, Ashvni Narayanan, Jonathan Spreer
The residual map as a stratified fibration over the resonance arrangement
Dawei Chen, Scott Mullane, Nick Salter et al.
Chromatic Spherical and Renormalized Reshetikhin-Turaev Invariants for Drinfeld Centers
Nicolas Bridges, Shawn Cui, Nathan Geer
3-manifold decision problems and Riemann hypotheses
John A. Baldwin, Steven Sivek
On the (in)finiteness of fixed characters in genus 3
Yixuan Fu
Non-Pseudo-Arithmetic Hyperbolic 4-Manifolds
Alexander Kolpakov