Cosmetic Surgery in Integral Homology $L$-Spaces

Abstract

Let $K$ be a non-trivial knot in $S^3$, and let $r$ and $r^{\prime }$ be two distinct rational numbers of same sign, allowing $r$ to be infinite; we prove that there is no orientation-preserving homeomorphism between the manifolds $S_r^3(K)$ and $S_{r^{\prime }}^3(K)$. We further generalize this uniqueness result to knots in arbitrary integral homology L-spaces.

References in corpus (2)

• Link Floer homology detects the Thurston norm
• Cosmetic surgeries on genus one knots

Cited by in corpus (4)

• Cosmetic surgeries on knots in $S^3$
• Exceptional Cosmetic surgeries on $S^3$
• Knot Complement Problem for L-space $\mathbb{Z}H{S}^3$
• $PS{L}_2(\mathbb{C})$-character varieties and Seifert fibered cosmetic surgeries