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arXiv · 2610.03411

Menger Curve and Non-Planar Boundaries in Quotients of Hyperbolic Groups

Rafaela Ioannou
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Abstract

We study the persistence of non-planarity in boundaries of hyperbolic groups under quotients, focusing on quotients by large enough powers of infinite order elements. We prove that the non-planarity of the boundary of a one-ended hyperbolic group is preserved under such quotients. As a consequence, we obtain an analogous result about the persistence of Menger curve boundaries.

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Rafaela Ioannou. 2026-10-02. Menger Curve and Non-Planar Boundaries in Quotients of Hyperbolic Groups. https://arxiv.org/abs/2610.03411

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