On loose Legendrian knots in rational homology spheres
arXiv:1707.04872 · doi:10.1016/j.topol.2017.12.025
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.