Year: 2024
Type: preprint
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.
Source: arXiv (Cornell University)
DOI: 10.17863/cam.125292
Author: Wilton, Henry
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7126065750
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