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arXiv · 2405.20428

Relatively hyperbolic groups with planar boundaries

G. Christopher Hruska·Genevieve S. Walsh
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Abstract

In this article, we prove a version of Martin and Skora's conjecture that convergence groups on the $2$-sphere are covered by Kleinian groups. Given a relatively hyperbolic group pair $(G,\mathcal{P})$ with planar boundary and no Sierpinski carpet or cut points in its boundary, and with $G$ one ended and virtually having no $2$-torsion, we show that $G$ is virtually Kleinian. We also give applications to various versions of the Cannon conjecture and to convergence groups acting on $S^2$.

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G. Christopher Hruska, Genevieve S. Walsh. 2024-05-30. Relatively hyperbolic groups with planar boundaries. https://arxiv.org/abs/2405.20428

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