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arXiv · 1909.05048

Connected sums of knots do not admit purely cosmetic surgeries

Ran Tao
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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 $S^3$ do not admit purely cosmetic surgeries. In this article, we confirm this conjecture for connected sums of knots by analysing the JSJ-structures.

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Ran Tao. 2019-09-11. Connected sums of knots do not admit purely cosmetic surgeries. https://arxiv.org/abs/1909.05048

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