Connectivity of Coxeter group Morse boundaries
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916655469166592 |
|---|---|
| author | Cordes, Matthew Levcovitz, Ivan |
| author_facet | Cordes, Matthew Levcovitz, Ivan |
| contents | We study the connectivity of Morse boundaries of Coxeter groups. We define two conditions on the defining graph of a Coxeter group: wide-avoidant and wide-spherical-avoidant. We show that wide-spherical-avoidant, one-ended, affine-free Coxeter groups have connected and locally connected Morse boundaries. On the other hand, one-ended Coxeter groups that are not wide-avoidant and not wide have disconnected Morse boundary. For the right-angled case, we get a full characterization: a one-ended right-angled Coxeter group has connected, non-empty Morse boundary if and only if it is wide-avoidant. Along the way we characterize Morse geodesic rays in affine-free Coxeter groups as those that spend uniformly bounded time in cosets of wide special subgroups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14085 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Connectivity of Coxeter group Morse boundaries Cordes, Matthew Levcovitz, Ivan Group Theory Geometric Topology 20F65, 20F67, 20F55 We study the connectivity of Morse boundaries of Coxeter groups. We define two conditions on the defining graph of a Coxeter group: wide-avoidant and wide-spherical-avoidant. We show that wide-spherical-avoidant, one-ended, affine-free Coxeter groups have connected and locally connected Morse boundaries. On the other hand, one-ended Coxeter groups that are not wide-avoidant and not wide have disconnected Morse boundary. For the right-angled case, we get a full characterization: a one-ended right-angled Coxeter group has connected, non-empty Morse boundary if and only if it is wide-avoidant. Along the way we characterize Morse geodesic rays in affine-free Coxeter groups as those that spend uniformly bounded time in cosets of wide special subgroups. |
| title | Connectivity of Coxeter group Morse boundaries |
| topic | Group Theory Geometric Topology 20F65, 20F67, 20F55 |
| url | https://arxiv.org/abs/2503.14085 |