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arXiv · 1707.04872

On loose Legendrian knots in rational homology spheres

Alberto Cavallo
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Abstract

We prove that loose Legendrian knots in a rational homology contact 3-sphere, satisfying some additional hypothesis, are Legendrian isotopic if and only if they have the same classical invariants. The proof requires a result of Dymara on loose Legendrian knots and Eliashberg's classification of overtwisted contact structures on 3-manifolds.

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Alberto Cavallo. 2017-07-16. On loose Legendrian knots in rational homology spheres. https://doi.org/10.1016/j.topol.2017.12.025

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