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Exceptional or half-integral chirally cosmetic surgeries

Kazuhiro Ichihara, Toshio Saito

Abstract

A pair of Dehn surgeries on a knot is called chirally cosmetic if they yield orientation-reversingly homeomorphic 3-manifolds. In this paper, we consider exceptional or half-integral chirally cosmetic surgeries, and obtain several restrictions.

Exceptional or half-integral chirally cosmetic surgeries

Abstract

A pair of Dehn surgeries on a knot is called chirally cosmetic if they yield orientation-reversingly homeomorphic 3-manifolds. In this paper, we consider exceptional or half-integral chirally cosmetic surgeries, and obtain several restrictions.
Paper Structure (3 sections, 6 theorems, 17 equations, 1 table)

This paper contains 3 sections, 6 theorems, 17 equations, 1 table.

Table of Contents

  1. Introduction
  2. Half-integral chirally cosmetic surgeries
  3. Chirally cosmetic exceptional surgery slopes

Key Result

Theorem 1

Let $K$ be a knot of genus $g$ in the 3-sphere $S^3$. For $p>0$, if $K(p) \cong - K(p/2)$, then $p \le 7 g+2$.

Theorems & Definitions (16)

  • Remark 1
  • Theorem 1
  • Theorem 2
  • proof : Proof of Theorem \ref{['thm1']}
  • Claim 1
  • proof
  • proof : Proof of Theorem \ref{['thm2']}
  • Remark 2
  • Theorem 3
  • Theorem 4
  • ...and 6 more