The SL(2,C) character variety of the one-holed torus
| dc.creator | Tan, Ser Peow | |
| dc.creator | Wong, Yan Loi | |
| dc.creator | Zhang, Ying | |
| dc.date | 2005-09-02 | |
| dc.date.accessioned | 2026-07-07T06:30:03Z | |
| dc.date.available | 2026-07-07T06:30:03Z | |
| dc.description | In this note we announce several results concerning the SL(2,C) character variety ${\mathcal X}$ of the one-holed torus. We give a description of the largest open subset ${\mathcal X}_{BQ}$ of ${\mathcal X}$ on which the mapping class group $Γ$ acts properly discontinuously, in terms of two very simple conditions, and show that a series identity generalizing McShane's identity for the punctured torus holds for all characters in this subset. We also give variations of the McShane-Bowditch identities to characters fixed by an Anosov element of $Γ$ with applications to closed hyperbolic three manifolds. Finally we give a definition of end invariants for SL(2,C) characters and give a partial classification of the set of end invariants of a character in ${\mathcal X}$. | |
| dc.description | 8 pages, announcement | |
| dc.identifier | https://arxiv.org/abs/math/0509033 | |
| dc.identifier | http://arxiv.org/abs/math/0509033 | |
| dc.identifier | Electron. Res. Announc. Amer. Math. Soc. 11 (2005) 103-110 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/98249 | |
| dc.subject | Geometric Topology | |
| dc.subject | Group Theory | |
| dc.subject | 32G15; 57M50; 30F60 | |
| dc.title | The SL(2,C) character variety of the one-holed torus | |
| dc.type | text |