Abstract
In this paper, the notion of the generic knots in contact 3-manifolds is introduced as an extension of that of the transversal knots. We show that any generic knots in contact 3-manifolds are constructed by perturbations of some Legendrian knots. As for the classification problem, the situation is completely different from the cases of the transversal and Legendrian knots. Two generic knots in a contact 3-manifold are generically isotopic if and only if they have the same number of non-transversal points and belong to the same topological knot class. We treat, in this paper, not only trivial knots in tight contact 3-manifolds but also non-trivial knots and those in overtwisted contact 3-manifolds.
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