The total Thurston-Bennequin number of complete and complete bipartite Legendrian graphs

Abstract

We study the Thurston-Bennequin number of complete and complete bipartite Legendrian graphs. We define a new invariant called the total Thurston-Bennequin number of the graph. We show that this invariant is determined by the Thurston-Bennequin numbers of 3-cycles for complete graphs and by the Thurston-Bennequin number of 4-cycles for complete bipartite graphs. We discuss the consequences of these results for K_4, K_5 and K_{3,3}.

arXiv comment17 pages, 16 figures