The agrarian polytope of two-generator one-relator groups

Henneke, Fabian; Kielak, Dawid

The agrarian polytope of two-generator one-relator groups

Henneke F, Kielak D (2020)
Journal of the London Mathematical Society. Second Series 102(2): 722-748.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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DOI

https://doi.org/10.1112/jlms.12334

URN

urn:nbn:de:0070-pub-29432961

Autor*in

Henneke, Fabian; Kielak, Dawid^UniBi

Einrichtung

Fakultät für Mathematik

Abstract / Bemerkung

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-Luck-Tillmann.

Stichworte

20J05 (primary); 12E15; 16S35; 20E06; 57Q10 (secondary)

Erscheinungsjahr

2020

Zeitschriftentitel

Journal of the London Mathematical Society. Second Series

Band

102

Ausgabe

Seite(n)

722-748

Urheberrecht / Lizenzen

Creative Commons Namensnennung-Nicht kommerziell 4.0 International (CC BY-NC 4.0)

ISSN

0024-6107

eISSN

1469-7750

Finanzierungs-Informationen

Open-Access-Publikationskosten wurden durch die Universität Bielefeld im Rahmen des DEAL-Vertrags gefördert.

Page URI

https://pub.uni-bielefeld.de/record/2943296

Zitieren

Henneke F, Kielak D. The agrarian polytope of two-generator one-relator groups. Journal of the London Mathematical Society. Second Series. 2020;102(2):722-748.

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

Henneke, Fabian, and Kielak, Dawid. 2020. “The agrarian polytope of two-generator one-relator groups”. Journal of the London Mathematical Society. Second Series 102 (2): 722-748.

Henneke, F., and Kielak, D. (2020). The agrarian polytope of two-generator one-relator groups. Journal of the London Mathematical Society. Second Series 102, 722-748.

Henneke, F., & Kielak, D., 2020. The agrarian polytope of two-generator one-relator groups. Journal of the London Mathematical Society. Second Series, 102(2), p 722-748.

F. Henneke and D. Kielak, “The agrarian polytope of two-generator one-relator groups”, Journal of the London Mathematical Society. Second Series, vol. 102, 2020, pp. 722-748.

Henneke, F., Kielak, D.: The agrarian polytope of two-generator one-relator groups. Journal of the London Mathematical Society. Second Series. 102, 722-748 (2020).

Henneke, Fabian, and Kielak, Dawid. “The agrarian polytope of two-generator one-relator groups”. Journal of the London Mathematical Society. Second Series 102.2 (2020): 722-748.

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