Tight fibered knots and band sums

Kenneth L. Baker, Kimihiko Motegi

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We give a short proof that if a non-trivial band sum of two knots results in a tight fibered knot, then the band sum is a connected sum. In particular, this means that any prime knot obtained by a non-trivial band sum is not tight fibered. Since a positive L-space knot is tight fibered, a non-trivial band sum never yields an L-space knot. Consequently, any knot obtained by a non-trivial band sum cannot admit a finite surgery. For context, we exhibit two examples of non-trivial band sums of tight fibered knots producing prime knots: one is fibered but not tight, and the other is strongly quasipositive but not fibered.

Original languageEnglish (US)
Pages (from-to)1357-1365
Number of pages9
JournalMathematische Zeitschrift
Volume286
Issue number3-4
DOIs
StatePublished - Aug 1 2017

Keywords

  • Band sum
  • L-space knot
  • Strongly quasipositive knot
  • Tight fibered knot

ASJC Scopus subject areas

  • Mathematics(all)

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