Knots that share four surgeries

Marc Kegel; Lisa Piccirillo

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arXiv · 2505.13168

Knots that share four surgeries

Marc Kegel·Lisa Piccirillo

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Abstract

Distinct knots K, K' can sometimes share a common p/q-framed Dehn surgery. A folk conjecture held that for a fixed pair of knots, this can occur for at most one value of p/q. We disprove this conjecture by constructing pairs of distinct knots K,K' that have common Dehn surgeries for four distinct slopes. We also construct non-isotopic Legendrian knots K,K' that have contactomorphic contact (+1)-and (-1)-surgeries, disproving an analogous conjecture in contact geometry.

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Marc Kegel, Lisa Piccirillo. 2025-05-19. Knots that share four surgeries. https://arxiv.org/abs/2505.13168

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