2014/04/30 by SJ, Paul A. Schweitzer, Souza, Fábio S.
#57M27 #57R17 #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1404.7732
All knots in R3 possess Seifert surfaces, and so the classical Thurston-Bennequin and rotation (or Maslov) invariants for Legendrian knots in a contact structure on R3 can be defined. The definitions extend easily to null-homologous knots in any 3-manifold M endowed with a contact structure ξ. We generalize the definition of Seifert surfaces and use them to define these invariants for all Legendrian knots, including those that are not null-homologous, in a contact structure on the 3-torus T3. We show how to compute the Thurston-Bennequin and rotation invariants in a tight oriented contact structure on T3 using projections.