Cosmetic contact surgeries along transverse knots and the knot complement problem

Marc Kegel

doi:10.1016/j.topol.2019.01.020

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arXiv · 1703.05596

Cosmetic contact surgeries along transverse knots and the knot complement problem

Marc Kegel

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Abstract

We study cosmetic contact surgeries along transverse knots in the standard contact 3-sphere, i.e. contact surgeries that yield again the standard contact 3-sphere. The main result is that we can exclude non-trivial cosmetic contact surgeries along all transverse knots not isotopic to the transverse unknot with self-linking number -1. As a corollary it follows that every transverse knot in the standard contact 3-sphere is determined by the contactomorphism type of its exteriors. Moreover, we give counterexamples to this for transverse links in the standard contact 3-sphere.

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Marc Kegel. 2017-03-16. Cosmetic contact surgeries along transverse knots and the knot complement problem. https://doi.org/10.1016/j.topol.2019.01.020

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