We prove a generalization of Bennequin’s inequality for Legendrian knots in a 3-dimensional contact manifold , under the assumption that is the boundary of a 4-dimensional manifold and the version of Seiberg-Witten invariants introduced by Kronheimer and Mrowka [Invent. Math. 130 (1997) 209–255] is nonvanishing. The proof requires an excision result for Seiberg-Witten moduli spaces; then the Bennequin inequality becomes a special case of the adjunction inequality for surfaces lying inside .
"Legendrian knots and monopoles." Algebr. Geom. Topol. 6 (1) 1 - 69, 2006. https://doi.org/10.2140/agt.2006.6.1