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arXiv · 2609.11627

Bounded vertical deviations and irrational circle factors in Dehn Twist classes

Heric Corrêa
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Abstract

We prove that any homeomorphism of the two-torus homotopic to a Dehn twist map with irrational bounded vertical deviations admits an irrational circle factor. This establishes a rigidity property previously studied by Kocsard, who proved this implication under the additional assumption of a small-wandering-domain hypothesis. We demonstrate that this hypothesis can be entirely dropped: the large-scale shear intrinsic to a Dehn twist naturally eliminates the general annular obstructions that cannot be removed in the homotopy class of the identity.

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Heric Corrêa. 2026-09-10. Bounded vertical deviations and irrational circle factors in Dehn Twist classes. https://arxiv.org/abs/2609.11627

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