A note on orientation-reversing distance one surgeries on non-null-homologous knots
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- by Tetsuya Ito;
- Proc. Amer. Math. Soc. 152 (2024), 4515-4519
- DOI: https://doi.org/10.1090/proc/16964
- Published electronically: August 26, 2024
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Abstract:
We show that there are no distance one surgeries on non-null-homologous knots in $M$ that yield $-M$ ($M$ with opposite orientation) if $M$ is a 3-manifold obtained by a Dehn surgery on a knot $K$ in $S^{3}$, such that the order of its first homology is divisible by $9$ but is not divisible by $27$.
As an application, we show several knots, including the $(2,9)$ torus knot, do not have chirally cosmetic bandings. This simplifies the proof of a result first proven by Yang that the $(2,k)$ torus knot $(k>1)$ has a chirally cosmetic banding if and only if $k=5$.
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Bibliographic Information
- Tetsuya Ito
- Affiliation: Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan
- MR Author ID: 922393
- ORCID: 0000-0001-8156-1341
- Email: tetitoh@math.kyoto-u.ac.jp
- Received by editor(s): November 20, 2023
- Received by editor(s) in revised form: March 24, 2024
- Published electronically: August 26, 2024
- Additional Notes: The author was partially supported by JSPS KAKENHI Grant Numbers 19K03490, 21H04428, 23K03110.
- Communicated by: Shelly Harvey
- © Copyright 2024 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 152 (2024), 4515-4519
- MSC (2020): Primary 57K10; Secondary 57K16, 57M12
- DOI: https://doi.org/10.1090/proc/16964