Hyperbolic isometries of the fine curve graph of higher genus surfaces

2023/11/02 by Guihéneuf, Pierre-Antoine, Militon, Emmanuel · 2 citations
#Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2311.01087

Abstract

We prove that for a homeomorphism f that is isotopic to the identity on a closed hyperbolic surface, the following are equivalent: * f acts hyperbolically on the fine curve graph; * f is isotopic to a pseudo-Anosov map relative to a finite f-invariant set; * the ergodic homological rotation set of f has nonempty interior.

Cited by

• Surface homeomorphisms with big rotation set
• Bounded deviations in higher genus I: closed geodesics

Related

• Hyperbolic Geometry and Homotopic Homeomorphisms of Surfaces
• Automorphisms of the fine curve graph
• Automorphisms of the fine curve graph
• Curves on 2-manifolds and isotopies
• Rotation sets and actions on curves