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Errata: A note on orientation-reversing distance one surgeries on non-null-homologous knots

Tetsuya Ito

Abstract

The author would like to report an error of [T. Ito, Proc. Amer. Math. Soc. 152 (2024), pp. 4515--4519.] (version 1 of the arXiv:2311.08676) )

Errata: A note on orientation-reversing distance one surgeries on non-null-homologous knots

Abstract

The author would like to report an error of [T. Ito, Proc. Amer. Math. Soc. 152 (2024), pp. 4515--4519.] (version 1 of the arXiv:2311.08676) )
Paper Structure (1 section, 4 theorems, 11 equations)

This paper contains 1 section, 4 theorems, 11 equations.

Table of Contents

  1. Acknowledgement

Key Result

Theorem 1

Let $Y$ be an L-space obtained by Dehn surgery on a knot in $S^{3}$, and that $|H_1(Y;\mathbb{Z})|= 9p_0$ with $p_0\not \equiv 0 \pmod{3}$. If $d(Y,\mathfrak{t}_Y) \neq 0,\pm 1$, then there are no distance one surgeries between $Y$ and $-Y$.

Theorems & Definitions (6)

  • Theorem 1
  • Theorem 2
  • proof : Proof of Theorem \ref{['theorem:main']}
  • Corollary 1
  • Corollary 2
  • proof : Proof of Theorem \ref{['theorem:main2']}