The volume of hyperbolic alternating link complements

• Autores: Marc Lackenby
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 88, Nº 1, 2004, págs. 204-224
• Idioma: inglés
• DOI: 10.1112/s0024611503014291
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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 $v_3(10t(D) - 10)$, 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.