arXiv:2311.01087 Abstract | arXiv Analytics

arXiv:2311.01087 [math.DS]Abstract References Reviews Resources

Hyperbolic isometries of the ne curve graph of higher genus surfaces

Pierre-Antoine Guihéneuf, Emmanuel Militon

Published 2023-11-02Version 1

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.

Categories: math.DS, math.GR, math.GT

Keywords: higher genus surfaces, hyperbolic isometries, fine curve graph, finite f-invariant set, ergodic homological rotation set

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