Mathematical Research Letters
Volume 19 (2012)
The Self-Linking Number in Planar Open Book Decompositions
Pages: 41 – 58
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 formula for braids in the standard contact $3$-sphere.