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arXiv · 2302.08184

Parabolic isometries of the fine curve graph of the torus

Pierre-Antoine Guiheneuf·Emmanuel Militon
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Abstract

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

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Pierre-Antoine Guiheneuf, Emmanuel Militon. 2023-02-16. Parabolic isometries of the fine curve graph of the torus. https://arxiv.org/abs/2302.08184

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