A group is tubular if it acts on a tree with vertex stabilizers and 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.
Cite this article
Daniel J. Woodhouse, Classifying virtually special tubular groups. Groups Geom. Dyn. 12 (2018), no. 2, pp. 679–702DOI 10.4171/GGD/452