Hyperbolic isometries of the fine curve graph of higher genus surfaces
Résumé
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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