Infinitely many knots admitting the same integer surgery

2014/07/06 by John Luecke, Luecke, John, John Osoinach +1 · 4 citations
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.1407.1529

7 pages, 4 figures

arxiv created 2014/07/06 · arxiv updated 2014/07/08

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 S³ 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 ≠ 0 the bridge numbers of the knots constructed tend to infinity as the number of twists along the annulus increases.

Cited by

• On the detection of knotted spheres by their traces in high dimensions
• Unique Surgery Descriptions along Knots
• Closures of 1-tangles and annulus twists
• Infinitely many knots admitting the same integer surgery and a 4-dimensional extension

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