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arXiv · 2603.20424

From cut sets to cube complexes

Matthew Haulmark·Jason Fox Manning
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Abstract

In this paper, we obtain an action on a cube complex from an action on a path-connected topological space with a system of divisions. In the settings of hyperbolic groups or relatively hyperbolic groups with no peripheral splittings, our result provides an alternate route to Sageev's construction of a cube complex action from a collection of (relatively) quasiconvex subgroups of a (relatively) hyperbolic group.

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Matthew Haulmark, Jason Fox Manning. 2026-03-20. From cut sets to cube complexes. https://arxiv.org/abs/2603.20424

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