Quasi-isometry classification of certain graph $2$-braid groups and its applications
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917923322331136 |
|---|---|
| author | An, Byung Hee Oh, Sangrok |
| author_facet | An, Byung Hee Oh, Sangrok |
| contents | In \cite{Oh22}, the second author defined a complex of groups decomposition of the fundamental group of a finitely generated 2-dimensional special group, called an \emph{intersection complex}, which is a quasi-isometry invariant. In this paper, using the theory of intersection complexes, we classify the class of 2-braid groups over graphs with circumference $\leq 1$ up to quasi-isometry. Moreover, we find a sufficient condition when such a graph 2-braid group is quasi-isometric to a right-angled Artin group or not. Finally, by applying the same method, we also find that there is an algorithm to determine whether two 4-braid groups over trees are quasi-isometric or not. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10366 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasi-isometry classification of certain graph $2$-braid groups and its applications An, Byung Hee Oh, Sangrok Group Theory Geometric Topology 20F65, 20F36, 20F67 (Primary) 57M60 (Secondary) In \cite{Oh22}, the second author defined a complex of groups decomposition of the fundamental group of a finitely generated 2-dimensional special group, called an \emph{intersection complex}, which is a quasi-isometry invariant. In this paper, using the theory of intersection complexes, we classify the class of 2-braid groups over graphs with circumference $\leq 1$ up to quasi-isometry. Moreover, we find a sufficient condition when such a graph 2-braid group is quasi-isometric to a right-angled Artin group or not. Finally, by applying the same method, we also find that there is an algorithm to determine whether two 4-braid groups over trees are quasi-isometric or not. |
| title | Quasi-isometry classification of certain graph $2$-braid groups and its applications |
| topic | Group Theory Geometric Topology 20F65, 20F36, 20F67 (Primary) 57M60 (Secondary) |
| url | https://arxiv.org/abs/2502.10366 |