Infinitely many knots admitting the same integer surgery

John Luecke; John Osoinach

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arXiv · 1407.1529

Infinitely many knots admitting the same integer surgery

John Luecke·John Osoinach

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Abstract

The construction of knots via annular twisting has been used to create families of knots yielding the same manifold via Dehn surgery. Prior examples have all involved Dehn surgery where the surgery slope is an integral multiple of 2. In this note we prove that for any integer $n$ there exist infinitely many different knots in $S^3$ such that $n$-surgery on those knots yields the same manifold. In particular, when $|n|=1$ homology spheres arise from these surgeries. In addition, when $n \neq 0$ the bridge numbers of the knots constructed tend to infinity as the number of twists along the annulus increases.

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BibTeX RIS

John Luecke, John Osoinach. 2014-07-06. Infinitely many knots admitting the same integer surgery. https://arxiv.org/abs/1407.1529

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