Legendrian theta-graphs
arXiv:1303.2128 · doi:10.2140/pjm.2014.270.191
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 theta-graph with all cycles unknotted. We show that these invariants are not enough to determine the Legendrian class of a topologically planar theta-graph. We define the transverse push-off of a Legendrian graph and we determine its self linking number for Legendrian theta-graphs. In the case of topologically planar theta-graphs, we prove that the topological type of the transverse push-off is that of a pretzel link.
19 pages, 17 figures