The classification of punctured-torus groups
| dc.creator | Minsky, Yair N. | |
| dc.date | 1998-07-01 | |
| dc.date | 1999-03-01 | |
| dc.date.accessioned | 2026-07-07T05:25:14Z | |
| dc.date.available | 2026-07-07T05:25:14Z | |
| dc.description | Thurston's ending lamination conjecture proposes that a finitely generated Kleinian group is uniquely determined (up to isometry) by the topology of its quotient and a list of invariants that describe the asymptotic geometry of its ends. We present a proof of this conjecture for punctured-torus groups. These are free two-generator Kleinian groups with parabolic commutator, which should be thought of as representations of the fundamental group of a punctured torus. As a consequence we verify the conjectural topological description of the deformation space of punctured-torus groups (including Bers' conjecture that the quasi-Fuchsian groups are dense in this space) and prove a rigidity theorem: two punctured-torus groups are quasi-conformally conjugate if and only if they are topologically conjugate. | |
| dc.description | 67 pages, published version | |
| dc.identifier | https://arxiv.org/abs/math/9807001 | |
| dc.identifier | http://arxiv.org/abs/math/9807001 | |
| dc.identifier | Ann. of Math. (2) 149 (1999), no. 2, 559-626 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77106 | |
| dc.subject | Geometric Topology | |
| dc.subject | Dynamical Systems | |
| dc.subject | 30F40 (Primary) 57M50 (Secondary) | |
| dc.title | The classification of punctured-torus groups | |
| dc.type | text |