Chirally Cosmetic Surgeries on Kinoshita-Terasaka and Conway knot families

2022/09/22 by Xiliu Yang, Yang, Xiliu
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2209.10723

openalex publication_date 2022/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we prove that a nontrivial Kinoshita-Terasaka or Conway knot does not admit chirally cosmetic surgeries, by calculating the finite type invariant of order 3.

Related

• The purely cosmetic surgery conjecture is true for the Kinoshita-Terasaka and Conway knot families
• Positive 2-bridge knots and chirally cosmetic surgeries
• A non-torus positive 2-bridge knot does not admit chirally cosmetic surgeries
• Special alternating knots with sufficiently many twist regions have no chirally cosmetic surgeries
• Exceptional or half-integral chirally cosmetic surgeries