Surgeries on torus knots, rational balls, and cabling

Paolo Aceto; Marco Golla; Kyle Larson; Ana G. Lecuona

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arXiv · 2008.06760

Surgeries on torus knots, rational balls, and cabling

Paolo Aceto·Marco Golla·Kyle Larson·Ana G. Lecuona

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Abstract

We classify which positive integral surgeries on positive torus knots bound rational homology balls. Additionally, for a given knot K we consider which cables K(p,q) admit integral surgeries that bound rational homology balls. For such cables, let S(K) be the set of corresponding rational numbers q/p. We show that S(K) is bounded for each K. Moreover, if n-surgery on K bounds a rational homology ball then n is an accumulation point for S(K).

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Paolo Aceto, Marco Golla, Kyle Larson, Ana G. Lecuona. 2020-08-15. Surgeries on torus knots, rational balls, and cabling. https://arxiv.org/abs/2008.06760

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