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arXiv · 2208.10421

A cubulation with no factor system

Sam Shepherd
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Abstract

The primary method for showing that a given cubulated group is hierarchically hyperbolic is by constructing a factor system on the cube complex. In this paper we show that such a construction is not always possible, namely we construct a cubulated group for which the cube complex does not have a factor system. We also construct a cubulated group for which the induced action on the contact graph is not acylindrical.

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Sam Shepherd. 2022-08-22. A cubulation with no factor system. https://doi.org/10.2140/agt.2025.25.255

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