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arXiv · 2509.26156

Rotation sets and axes in the fine curve graph for torus homeomorphisms

Sebastian Hensel·Frédéric Le Roux
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Abstract

We expand the dictionary between the action of a torus homeomorphism on the fine curve graph and its rotation set. More precisely, we show that the fixed points at infinity of a loxodromic element determine the rotation set up to scale. A key ingredient is a metric version of the classical WPD property from geometric group theory. As a consequence we find new stable criteria for positive scl, and for two homeomorphisms to generate a free group, and we provide a Tits alternative for groups of torus homeomorphisms.

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Sebastian Hensel, Frédéric Le Roux. 2025-09-30. Rotation sets and axes in the fine curve graph for torus homeomorphisms. https://arxiv.org/abs/2509.26156

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