Abstract
An elementary stabilization of a Legendrian link L in the spherical cotangent bundle ST M of a surface M is a surgery that results in attaching a handle to M along two discs away from the image in M of the projection of the link L. A virtual Legendrian isotopy is a composition of stabilizations, destabilizations and Legendrian isotopies. We study virtual Legendrian isotopy classes of Legendrian links and show that every such class contains a unique irreducible representative. In particular we get a solution to the following conjecture of Cahn, Levi and the rst author: two Legendrian knots in ST S 2 that are isotopic as virtual Legendrian knots must be Legendrian isotopic in ST S 2 :
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