Dynamics on the SU(2,1)-character variety of the one-holed torus
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915238697238528 |
|---|---|
| author | Lawton, Sean Maloni, Sara Palesi, Frédéric |
| author_facet | Lawton, Sean Maloni, Sara Palesi, Frédéric |
| contents | We study the relative SU(2,1)-character varieties of the one-holed torus, and the action of the mapping class group on them. We use an explicit description of the character variety of the free group of rank two in SU(2,1) in terms of traces, which allow us to describe the topology of the character variety. We then combine this description with a generalization of the Farey graph adapted to this new combinatorial setting, using ideas introduced by Bowditch. Using these tools, we can describe an open domain of discontinuity for the action of the mapping class group which strictly contains the set of convex cocompact characters, and we give several characterizations of representations in this domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10838 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamics on the SU(2,1)-character variety of the one-holed torus Lawton, Sean Maloni, Sara Palesi, Frédéric Geometric Topology Dynamical Systems Representation Theory Primary 57M60, 14M35, Secondary 57M50, 57K20 We study the relative SU(2,1)-character varieties of the one-holed torus, and the action of the mapping class group on them. We use an explicit description of the character variety of the free group of rank two in SU(2,1) in terms of traces, which allow us to describe the topology of the character variety. We then combine this description with a generalization of the Farey graph adapted to this new combinatorial setting, using ideas introduced by Bowditch. Using these tools, we can describe an open domain of discontinuity for the action of the mapping class group which strictly contains the set of convex cocompact characters, and we give several characterizations of representations in this domain. |
| title | Dynamics on the SU(2,1)-character variety of the one-holed torus |
| topic | Geometric Topology Dynamical Systems Representation Theory Primary 57M60, 14M35, Secondary 57M50, 57K20 |
| url | https://arxiv.org/abs/2402.10838 |