Links with no exceptional surgeries
By David Futer, Jessica S. Purcell. 2004
57 citations recorded by the source corpus.
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.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/191104f5861869a687073eed5646e55ddede746d
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- An introduction to fully augmented links (2011, methodology): “These have been used to bound exceptional surgeries on knots [7], volumes of knots [6], and cusp shapes [13].”