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arXiv · 2406.02121

Surface groups among cubulated hyperbolic and one-relator groups

Henry Wilton
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Abstract

Let $X$ be a non-positively curved cube complex with hyperbolic fundamental group. We prove that $\pi_1(X)$ has a non-free subgroup of infinite index unless $\pi_1(X)$ is either free or a surface group, answering questions of Gromov and Whyte (in a special case) and Wise. A similar result for one-relator groups follows, answering a question posed by several authors. The proof relies on a careful analysis of free and cyclic splittings of cubulated groups.

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Henry Wilton. 2024-06-04. Surface groups among cubulated hyperbolic and one-relator groups. https://arxiv.org/abs/2406.02121

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