The volume of hyperbolic alternating link complements

  title={The volume of hyperbolic alternating link complements},
  author={Marc Lackenby},
  journal={Proceedings of The London Mathematical Society},
  • M. Lackenby
  • Published 2000
  • Mathematics
  • Proceedings of The London Mathematical Society
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… Expand
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