English

The agrarian polytope of two-generator one-relator groups

Algebraic Topology 2020-04-29 v1 Group Theory

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-L\"uck-Tillmann.

Keywords

Cite

@article{arxiv.1912.04650,
  title  = {The agrarian polytope of two-generator one-relator groups},
  author = {Fabian Henneke and Dawid Kielak},
  journal= {arXiv preprint arXiv:1912.04650},
  year   = {2020}
}

Comments

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