The agrarian polytope of two-generator one-relator groups

2019/12/10 by Fabian Henneke, Dawid Kielak · 1 citation
Mathematics · #math.AT #math.GR #msc:20J05 #msc:12E15 #msc:16S35 #msc:20E06 #msc:57Q10

paper · pdf · doi:10.1112/jlms.12334

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

arxiv created 2019/12/10 · arxiv updated 2020/04/29

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.

Citations

• Agrarian and L²-invariants

Cited by

• The word problem for two-generator one-relator inverse monoids