Links with no exceptional surgeries

David Futer; Jessica S. Purcell

doi:10.4171/cmh/105

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arXiv · math/0412307

Links with no exceptional surgeries

David Futer·Jessica S. Purcell

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Abstract

We show that if a knot admits a prime, twist-reduced diagram with at least 4 twist regions and at least 6 crossings per twist region, then every non-trivial Dehn filling of that knot is hyperbolike. A similar statement holds for links. We prove this using two arguments, one geometric and one combinatorial. The combinatorial argument further implies that every link with at least 2 twist regions and at least 6 crossings per twist region is hyperbolic and gives a lower bound for the genus of a link.

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David Futer, Jessica S. Purcell. 2004-12-15. Links with no exceptional surgeries. https://doi.org/10.4171/cmh/105

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