The agrarian polytope of two‐generator one‐relator groups

Relying on the theory of agrarian invariants introduced in previous work, we
solve a conjecture of Friedl-Tillmann: we show that the marked polytopes they
constructed for two-generator one-relator groups with nice presentations are
independent of the presentations used. We also show that, when the groups are
additionally torsion-free, the agrarian polytope encodes the splitting
complexity of the group. This generalises theorems of Friedl-Tillmann and
Friedl-L\"uck-Tillmann.