Property (QT) for 3-manifold groups
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2021
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910868080427008 |
|---|---|
| author | Han, Suzhen Nguyen, Hoang Thanh Yang, Wenyuan |
| author_facet | Han, Suzhen Nguyen, Hoang Thanh Yang, Wenyuan |
| contents | According to Bestvina-Bromberg-Fujiwara, a finitely generated group is said to have property (QT) if it acts isometrically on a finite product of quasi-trees so that orbital maps are quasi-isometric embeddings. We prove that the fundamental group $π_1(M)$ of a compact, connected, orientable 3-manifold $M$ has property (QT) if and only if no summand in the sphere-disc decomposition of $M$ supports either Sol or Nil geometry. In particular, all compact, orientable, irreducible 3-manifold groups with nontrivial torus decomposition and not supporting Sol geometry have property (QT). In the course of our study, we establish property (QT) for the class of Croke-Kleiner admissible groups and of relatively hyperbolic groups under natural assumptions has property (QT). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_03361 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Property (QT) for 3-manifold groups Han, Suzhen Nguyen, Hoang Thanh Yang, Wenyuan Geometric Topology Group Theory According to Bestvina-Bromberg-Fujiwara, a finitely generated group is said to have property (QT) if it acts isometrically on a finite product of quasi-trees so that orbital maps are quasi-isometric embeddings. We prove that the fundamental group $π_1(M)$ of a compact, connected, orientable 3-manifold $M$ has property (QT) if and only if no summand in the sphere-disc decomposition of $M$ supports either Sol or Nil geometry. In particular, all compact, orientable, irreducible 3-manifold groups with nontrivial torus decomposition and not supporting Sol geometry have property (QT). In the course of our study, we establish property (QT) for the class of Croke-Kleiner admissible groups and of relatively hyperbolic groups under natural assumptions has property (QT). |
| title | Property (QT) for 3-manifold groups |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2108.03361 |