Strongly aperiodic SFTs on generalized Baumslag–Solitar groups

We look at constructions of aperiodic subshifts of finite type (SFTs) on fundamental groups of graph of groups. In particular, we prove that all generalized Baumslag-Solitar groups (GBS) admit a strongly aperiodic SFT. Our proof is based on a structural theorem by Whyte and on two constructions of strongly aperiodic SFTs on F_n × Z and BS(m, n) of our own. Our two constructions rely on a path-folding technique that lifts an SFT on Z² inside an SFT on F_n × Z or an SFT on the hyperbolic plane inside an SFT on BS(m, n). In the case of F_n × Z, the path folding technique also preserves minimality, so that we get minimal strongly aperiodic SFTs on unimodular GBS groups.