Links with no exceptional surgeries

Details Links with no exceptional surgeries Links with no exceptional surgeries

2004-12-15

arxiv.org/abs/math/0412307v3

Commentarii Mathematici Helvetici 82 (2007), No. 3, 629-664

Mathematics

Geometric Topology

28 pages, 15 figures. Minor rewording and organizational changes; also added theorem giving a lower bound on the genus of thes

Scientific paper

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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