Article Dans Une Revue Proceedings of the London Mathematical Society Année : 2024

Parabolic isometries of the fine curve graph of the torus

Résumé

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 in [BHM + 22]. This is made by proving that if $f \in Homeo(\mathbf T^2)$, then f acts elliptically on $C^\dagger(\mathbf T^2)$ if and only if f has bounded deviation from some $v\in\mathbf Q^2\setminus \{0\}$. The proof involves some kind of slow rotation sets for torus homeomorphisms.

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Dates et versions

hal-03989880 , version 1 (15-02-2023)
hal-03989880 , version 2 (13-05-2023)

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Pierre‐antoine Guihéneuf, Emmanuel Militon. Parabolic isometries of the fine curve graph of the torus. Proceedings of the London Mathematical Society, 2024, 129 (2), ⟨10.1112/plms.12625⟩. ⟨hal-03989880v2⟩
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