Chirally cosmetic surgeries and Casson invariants

2017/07/01 by Kazuhiro Ichihara, Tetsuya Ito, Ichihara, Kazuhiro +3
Biochemistry, Genetics and Molecular Biology · Mathematics · #Connective tissue disorders research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1707.00152

openalex publication_date 2017/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study chirally cosmetic surgeries, that is, a pair of Dehn surgeries on a knot producing homeomorphic 3-manifolds with opposite orientations. Several constraints on knots and surgery slopes to admit such surgeries are given. Our main ingredients are the original and the SL(2,ℂ) version of Casson invariants. As applications, we give a complete classification of chirally cosmetic surgeries on alternating knots of genus one.

Citations

• Boundary slopes and the numbers of positive/negative crossings for Montesinos knots
• CLOSED 3–MANIFOLDS UNCHANGED BY DEHN SURGERY
• Dehn Surgery on Knots

Related

• Exceptional or half-integral 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
• Cosmetic surgeries on knots in homology spheres and the Casson--Walker invariant
• Cosmetic surgeries on knots in S³