### 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 language | English (US) |
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Pages (from-to) | 1-9 |

Number of pages | 9 |

Journal | Mathematische Zeitschrift |

DOIs | |

State | Accepted/In press - Nov 7 2016 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Mathematische Zeitschrift*, 1-9. https://doi.org/10.1007/s00209-016-1804-9

**Tight fibered knots and band sums.** / Baker, Kenneth; Motegi, Kimihiko.

Research output: Contribution to journal › Article

*Mathematische Zeitschrift*, pp. 1-9. https://doi.org/10.1007/s00209-016-1804-9

}

TY - JOUR

T1 - Tight fibered knots and band sums

AU - Baker, Kenneth

AU - Motegi, Kimihiko

PY - 2016/11/7

Y1 - 2016/11/7

N2 - 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.

AB - 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.

KW - Band sum

KW - L-space knot

KW - Strongly quasipositive knot

KW - Tight fibered knot

UR - http://www.scopus.com/inward/record.url?scp=84994476615&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84994476615&partnerID=8YFLogxK

U2 - 10.1007/s00209-016-1804-9

DO - 10.1007/s00209-016-1804-9

M3 - Article

AN - SCOPUS:84994476615

SP - 1

EP - 9

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

SN - 0025-5874

ER -