On the rotation class of knotted Legendrian tori in R5
In this paper we show how to combinatorially compute the rotation class of a large family of embedded Legendrian tori in R5 with the standard contact form. In particular, we give a formula to compute the Maslov index for any loop on the torus and compute the Maslov number of the Legendrian torus. These formulas are a necessary component in computing contact homology. Our methods use a new way to represent knotted Legendrian tori called Lagrangian hypercube diagrams.
Topology and its Applications
Baldridge, S., & McCarty, B. (2016). On the rotation class of knotted Legendrian tori in R5. Topology and its Applications, 209, 91-114. https://doi.org/10.1016/j.topol.2016.05.014