Parabolic isometries of the fine curve graph of the torus

2024/07/31 by Pierre‐Antoine Guihéneuf, Emmanuel Militon · 1 citation
Mathematics · #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Geometric Analysis and Curvature Flows

paper · doi:10.1112/plms.12625

Abstract

Abstract In this article, we finish the classification of actions of torus homeomorphisms on the fine curve graph initiated by Bowden, Hensel, Mann, Militon, and Webb. This is made by proving that if , then acts elliptically on if and only if has bounded deviations in some direction . The proof involves some kind of slow rotation sets for torus homeomorphisms.

Citations

• Rotation Sets for Maps of Tori
• Curves on 2-manifolds and isotopies
• A mixing-like property and inexistence of invariant foliations for minimal diffeomorphisms of the 2-torus
• Rotation sets and actions on curves

Cited by

• Bounded deviations in higher genus I: closed geodesics

Related

• Parabolic isometries of the fine curve graph of the torus
• Rotation sets and actions on curves
• Rotation sets and axes in the fine curve graph for torus homeomorphisms
• Torus diffeomorphisms with parabolic and non-proper actions on the fine curve graph and their generalized rotation sets
• Hyperbolic isometries of the fine curve graph of higher genus surfaces