Groups, Geometry, and Dynamics

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Volume 12, Issue 2, 2018, pp. 679–702
DOI: 10.4171/GGD/452

Published online: 2018-06-04

Classifying virtually special tubular groups

Daniel J. Woodhouse[1]

(1) Technion - Israel Institute of Technology, Haifa, Israel

A group is tubular if it acts on a tree with $\mathbb{Z}^2$ vertex stabilizers and $\mathbb{Z}$ edge stabilizers. We prove that a tubular group is virtually special if and only if it acts freely on a locally finite CAT(0) cube complex. Furthermore, we prove that if a tubular group acts freely on a finite dimensional CAT(0) cube complex, then it virtually acts freely on a three dimensional CAT(0) cube complex.

Keywords: CAT(0) cube complex, tubular group, virtually special, graphs of groups

Woodhouse Daniel: Classifying virtually special tubular groups. Groups Geom. Dyn. 12 (2018), 679-702. doi: 10.4171/GGD/452