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Journal Article

The agrarian polytope of two-generator one-relator groups

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Henneke,  Fabian
Max Planck Institute for Mathematics, Max Planck Society;

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Citation

Henneke, F., & Kielak, D. (2020). The agrarian polytope of two-generator one-relator groups. Journal of the London Mathematical Society, 102(2), 722-748. doi:10.1112/jlms.12334.


Cite as: http://hdl.handle.net/21.11116/0000-0006-9E42-E
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.