Cable knots do not admit cosmetic surgeries
Ran Tao

TL;DR
This paper proves that cable knots in the 3-sphere do not admit purely cosmetic Dehn surgeries, confirming Gordon's conjecture for this class of knots.
Contribution
It establishes that non-trivial cable knots cannot have purely cosmetic surgeries, advancing the understanding of Dehn surgery uniqueness.
Findings
Cable knots do not admit purely cosmetic surgeries
Confirms Gordon's conjecture for cable knots
Supports the uniqueness of Dehn surgeries on non-trivial knots
Abstract
Two Dehn surgeries on a knot are called purely cosmetic if their surgered manifolds are homeomorphic as oriented manifolds. Gordon conjectured that non-trivial knots in do not admit purely cosmetic surgeries. In this article, we confirm this conjecture for cable knots.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics
