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arXiv · 1510.05049

Restrictions on rotation sets for commuting torus homeomorphisms

Deissy Milena Sotelo Castelblanco
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Abstract

Let $K_1$, $K_2$ $\subset$ $R^2$ be two convex, compact sets. We would like to know if there are commuting torus homeomorphisms $f$ and $h$ homotopic to the identity, with lifts $\tilde f$ and $\tilde h$, such that $K_1$ and $K_2$ are their rotation sets, respectively. In this work, we proof some cases where it cannot happen, assuming some restrictions on rotation sets.

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Deissy Milena Sotelo Castelblanco. 2015-10-16. Restrictions on rotation sets for commuting torus homeomorphisms. https://arxiv.org/abs/1510.05049

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