JournalscmhVol. 82 , No. 3DOI 10.4171/cmh/105

Links with no exceptional surgeries

  • David Futer

    Michigan State University, East Lansing, United States
  • Jessica S. Purcell

    University of Texas at Austin, United States
Links with no exceptional surgeries cover

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.