The Self-Linking Number in Planar Open Book Decompositions
  We construct a Seifert surface for a given null-homologous transverse link in a contact manifold that is compatible with a planar open book decomposition, then obtain a formula of the self-linking number. It extends Bennequin's self-linking number formula for braids in the standard contact 3-sphere. 
Keiko Kawamuro
math.GT