The self-linking number in annulus and pants open book decompositions

Kawamuro, Keiko; Pavelescu, Elena

doi:10.2140/agt.2011.11.553

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The self-linking number in annulus and pants open book decompositions

Keiko Kawamuro and Elena Pavelescu

Algebraic & Geometric Topology 11 (2011) 553–585

DOI: 10.2140/agt.2011.11.553

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.

Keywords

braid, transverse knots, self-linking number

Mathematical Subject Classification 2000

Primary: 57M25, 57M27

Secondary: 57M50

References

Publication

Received: 8 November 2009

Revised: 6 October 2010

Accepted: 24 October 2010

Published: 15 February 2011

Authors

Keiko Kawamuro
Department of Mathematics University of Iowa 14 MacLean Hall Iowa City IA 52242 USA

Elena Pavelescu
Department of Mathematics Rice University 6100 Main St Houston, TX 77005 USA

Volume 11, issue 1 (2011)