Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2601.15140 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914379249745920 |
|---|---|
| author | Weis, Jannis |
| author_facet | Weis, Jannis |
| contents | We prove that homological filling functions over a ring $R$ equipped with the discrete norm are quasi-isometry invariants for all groups of type $\mathrm{FP}_n$. This confirms a conjecture of Bader-Kropholler-Vankov in the case of discrete norms. The proof uses a technique of equipping free chain complexes with a geometric structure, allowing for analogues of cellular constructions in the purely algebraic setting. As a further application we prove quasi-isometry invariance for a weighted version of integral and discrete filling functions originally introduced in the study of the rapid decay property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15140 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quasi-Isometry Invariance of discrete Higher Filling Functions Weis, Jannis Group Theory Metric Geometry 20F69 (Primary) 20F65, 05C25 (Secondary) We prove that homological filling functions over a ring $R$ equipped with the discrete norm are quasi-isometry invariants for all groups of type $\mathrm{FP}_n$. This confirms a conjecture of Bader-Kropholler-Vankov in the case of discrete norms. The proof uses a technique of equipping free chain complexes with a geometric structure, allowing for analogues of cellular constructions in the purely algebraic setting. As a further application we prove quasi-isometry invariance for a weighted version of integral and discrete filling functions originally introduced in the study of the rapid decay property. |
| title | Quasi-Isometry Invariance of discrete Higher Filling Functions |
| topic | Group Theory Metric Geometry 20F69 (Primary) 20F65, 05C25 (Secondary) |
| url | https://arxiv.org/abs/2601.15140 |