The volume of hyperbolic alternating link complements
| dc.creator | Lackenby, Marc | |
| dc.date | 2000-12-19 | |
| dc.date | 2003-06-16 | |
| dc.date.accessioned | 2026-07-07T04:39:18Z | |
| dc.date.available | 2026-07-07T04:39:18Z | |
| dc.description | If a hyperbolic link has a prime alternating diagram D, then we show that the link complement's volume can be estimated directly from D. We define a very elementary invariant of the diagram D, its twist number t(D), and show that the volume lies between v_3(t(D) - 2)/2 and v_3(16t(D) - 16), where v_3 is the volume of a regular hyperbolic ideal 3-simplex. As a consequence, the set of all hyperbolic alternating and augmented alternating link complements is a closed subset of the space of all complete finite volume hyperbolic 3-manifolds, in the geometric topology. The appendix by Ian Agol and Dylan Thurston, which was written after the first version of this paper was distributed, improves the upper bound on volume to v_3(10t(D) - 10). In addition, examples of alternating links are given which asymptotically achieve this bound. | |
| dc.description | 30 pages, 17 figures; contains an appendix by Ian Agol and Dylan Thurston | |
| dc.identifier | https://arxiv.org/abs/math/0012185 | |
| dc.identifier | http://arxiv.org/abs/math/0012185 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60609 | |
| dc.subject | Geometric Topology | |
| dc.subject | Differential Geometry | |
| dc.subject | 57M25; 57N10 | |
| dc.title | The volume of hyperbolic alternating link complements | |
| dc.type | text |