Tight fibered knots and band sums

Kenneth L. Baker; Kimihiko Motegi

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arXiv · 1509.00121

Tight fibered knots and band sums

Kenneth L. Baker·Kimihiko Motegi

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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.

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BibTeX RIS

Kenneth L. Baker, Kimihiko Motegi. 2015-09-01. Tight fibered knots and band sums. https://arxiv.org/abs/1509.00121

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