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arXiv · 1604.05196

The Legendrian knot complement problem

Marc Kegel
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Abstract

We prove that every Legendrian knot in the tight contact structure of the 3-sphere is determined by the contactomorphism type of its exterior. Moreover, by giving counterexamples we show this to be not true for Legendrian links in the tight 3-sphere. On the way a new user-friendly formula for computing the Thurston-Bennequin invariant of a Legendrian knot in a surgery diagram is given.

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Marc Kegel. 2016-04-18. The Legendrian knot complement problem. https://doi.org/10.1142/s0218216518500670

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