LEGENDRIAN θ−GRAPHS

Abstract. In this article we give necessary and sufficient conditions for two triples of integers to be realized as the Thurston-Bennequin number and the rotation number of a Legendrian θ−graph with all cycles unknotted. We show that these invariants are not enough to determine the Legendrian class of a topologically planar θ−graph. We define the transverse push-off of a Legendrian graph and we determine its self linking number for Legendrian θ−graphs. In the case of topologically planar θ−graphs, we prove that the topological type of the transverse push-off is that of a pretzel link. 1