The agrarian polytope of two‐generator one‐relator groups
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 g...
| Auteurs principaux: | , |
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| Format: | Journal article |
| Langue: | English |
| Publié: |
Wiley
2020
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| _version_ | 1826277602708422656 |
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| author | Henneke, F Kielak, D |
| author_facet | Henneke, F Kielak, D |
| author_sort | Henneke, F |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T23:31:23Z |
| format | Journal article |
| id | oxford-uuid:6c234a34-4584-4aef-a6b9-c08dd5bf8b51 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T23:31:23Z |
| publishDate | 2020 |
| publisher | Wiley |
| record_format | dspace |
| spelling | oxford-uuid:6c234a34-4584-4aef-a6b9-c08dd5bf8b512022-03-26T19:08:55ZThe agrarian polytope of two‐generator one‐relator groupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:6c234a34-4584-4aef-a6b9-c08dd5bf8b51EnglishSymplectic ElementsWiley2020Henneke, FKielak, DRelying 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. |
| spellingShingle | Henneke, F Kielak, D The agrarian polytope of two‐generator one‐relator groups |
| title | The agrarian polytope of two‐generator one‐relator groups |
| title_full | The agrarian polytope of two‐generator one‐relator groups |
| title_fullStr | The agrarian polytope of two‐generator one‐relator groups |
| title_full_unstemmed | The agrarian polytope of two‐generator one‐relator groups |
| title_short | The agrarian polytope of two‐generator one‐relator groups |
| title_sort | agrarian polytope of two generator one relator groups |
| work_keys_str_mv | AT hennekef theagrarianpolytopeoftwogeneratoronerelatorgroups AT kielakd theagrarianpolytopeoftwogeneratoronerelatorgroups AT hennekef agrarianpolytopeoftwogeneratoronerelatorgroups AT kielakd agrarianpolytopeoftwogeneratoronerelatorgroups |