The agrarian polytope of two-generator one-relator groups

Abstract

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-Lück-Tillmann.

26 pages; split off from arXiv:1809.08470v1 with the first part available as arXiv:1809.08470v2