Tubular free by cyclic groups act freely on CAT(0) cube complexes

Abstract

We identify when a tubular group (the fundamental group of a finite graph of groups with $\mathbb{Z}$$^{2}$ vertex and $\mathbb{Z}$ edge groups) is free by cyclic and show, using Wise's equitable sets criterion, that every tubular free by cyclic group acts freely on a CAT(0) cube complex.