Mathematical Research Letters

Volume 19 (2012)

Number 1

The Self-Linking Number in Planar Open Book Decompositions

Pages: 41 – 58



Keiko Kawamuro (Department of Mathematics, The University of Iowa, Iowa City, IA 52240, USA)


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.

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