We establish an upper bound for the Thurston–Bennequin number of a Legendrian link using the Khovanov homology of the underlying topological link. This bound is sharp in particular for all alternating links, and knots with nine or fewer crossings.
"A Legendrian Thurston–Bennequin bound from Khovanov homology." Algebr. Geom. Topol. 5 (4) 1637 - 1653, 2005. https://doi.org/10.2140/agt.2005.5.1637