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arXiv · 2311.01087

Hyperbolic isometries of the fine curve graph of higher genus surfaces

Pierre-Antoine Guihéneuf·Emmanuel Militon
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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.

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Pierre-Antoine Guihéneuf, Emmanuel Militon. 2023-11-02. Hyperbolic isometries of the fine curve graph of higher genus surfaces. https://arxiv.org/abs/2311.01087

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