Dehn surgery functions are never injective

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.

25 pages, 20 figures

Keywords

Geometric Topology, FOS: Mathematics, Geometric Topology (math.GT), 57K10, 57K14, 57K30

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