Links with no exceptional surgeries

David Futer, Jessica S. Purcell

Research output: Contribution to journalArticleResearchpeer-review

22 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)629-664
Number of pages36
JournalCommentarii Mathematici Helvetici
Issue number3
Publication statusPublished - 1 Jan 2007
Externally publishedYes


  • Dehn filling
  • Dehn surgery
  • Hyperbolic 3-manifolds
  • Knot complements
  • Link complements

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