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arXiv · 2508.13369

Dehn surgery functions are never injective

Kyle Hayden·Lisa Piccirillo·Laura Wakelin
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Abstract

We prove that, for each fixed rational number $p/q \in \mathbb{Q}$, there exists a pair of distinct knots whose $p/q$-surgeries are orientation-preservingly homeomorphic. This confirms a 1978 conjecture of Gordon.

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Kyle Hayden, Lisa Piccirillo, Laura Wakelin. 2025-08-18. Dehn surgery functions are never injective. https://arxiv.org/abs/2508.13369

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