The Self-Linking Number in Annulus and Pants Open Book Decompositions

Abstract

We find a self-linking number formula for a given null-homologous transverse link in a contact manifold that is compatible with either an annulus or a pair of pants open book decomposition. It extends Bennequin's self-linking formula for a braid in the standard contact $3$-sphere.

28 pages, 27 figures

References in corpus (2)

• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• Overtwisted open books from sobering arcs

Cited by in corpus (6)

• Open Book Foliations
• Bridge trisections in ${\mathbb{CP}}^2$ and the Thom conjecture (with Corrigendum)
• Braiding Knots in Contact 3-Manifolds
• On the self-linking number of transverse links
• Fibered knots and links in lens spaces
• On a relation between the self-linking number and the braid index of closed braids in open books