Chirally Cosmetic Surgeries on Kinoshita-Terasaka and Conway knot families
Xiliu Yang
TL;DR
This paper proves that certain complex knots, specifically Kinoshita-Terasaka and Conway knots, do not admit chirally cosmetic surgeries, using finite type invariants of order 3 to establish this non-existence.
Contribution
It introduces a novel application of finite type invariants of order 3 to demonstrate the non-existence of chirally cosmetic surgeries on these knots.
Findings
Kinoshita-Terasaka and Conway knots do not admit chirally cosmetic surgeries
Finite type invariant of order 3 is effective in this context
Provides a new method for analyzing cosmetic surgeries on knots
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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Advanced Combinatorial Mathematics