Seifert fibred knot manifolds

J. A. Hillman, J. Howie

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Abstract

We consider the question of when is the closed manifold obtained by elementary surgery on an n-knot Seifert fibered over a 2-orbifold. The possible bases are strongly constrained by the fact that knot groups have weight 1. We present a new family of 2-knots with solvable groups, overlooked in earlier work. The knots in this new family are neither invertible nor amphicheiral, and the weight orbits for the knot groups are parametrized by Z. There are no known examples in higher dimensions.

Original languageEnglish
Article number1350082
Number of pages17
JournalJournal of Knot Theory and its Ramifications
Volume22
Issue number14
DOIs
Publication statusPublished - Dec 2013

Keywords

  • 0-framed surgery
  • n-knot
  • 2-orbifold
  • Seifert fibred
  • solvable 2-knot group

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