Geodesic
A cubulation with no factor system
Shepherd, Sam1
1Institut für Mathematische Logik und Grundlagenforschung, Fachbereich Mathematik und Informatik, Universität Münster, Münster, Germany
Algebraic and Geometric Topology, Tome 25 (2025) no. 1, pp. 255-266
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The primary method for showing that a given cubulated group is hierarchically hyperbolic is by constructing a factor system on the cube complex. 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.

DOI : 10.2140/agt.2025.25.255
Keywords: CAT(0) cube complex, cubulated group, factor system, contact graph, acylindrical

Shepherd, Sam  1

1 Institut für Mathematische Logik und Grundlagenforschung, Fachbereich Mathematik und Informatik, Universität Münster, Münster, Germany 
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Shepherd, Sam. A cubulation with no factor system. Algebraic and Geometric Topology, Tome 25 (2025) no. 1, pp. 255-266. doi: 10.2140/agt.2025.25.255

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