Computing the Thurston-Bennequin invariant in open books
  We give explicit formulas and algorithms for the computation of the Thurston-Bennequin invariant of a nullhomologous Legendrian knot on a page of a contact open book and on contact Heegaard surfaces. Furthermore, we extend the results to rationally nullhomologous knots in arbitrary 3-manifolds. 
Sebastian Durst, Marc Kegel, and Mirko Klukas
math.GT math.SG