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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.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1112/jlms.12334

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Hertford College
Role:
Author
ORCID:
0000-0002-5536-9070
Publisher:
Wiley
Journal:
Journal of the London Mathematical Society More from this journal
Volume:
102
Issue:
2
Pages:
722-748
Publication date:
2020-04-22
Acceptance date:
2019-12-09
DOI:
EISSN:
1469-7750
ISSN:
0024-6107
Language:
English
Keywords:
Pubs id:
1118443
Local pid:
pubs:1118443
Deposit date:
2020-07-13

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