Algebraic & Geometric Topology

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

Keiko Kawamuro and Elena Pavelescu

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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.

Article information

Algebr. Geom. Topol., Volume 11, Number 1 (2011), 553-585.

Received: 8 November 2009
Revised: 6 October 2010
Accepted: 24 October 2010
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M27: Invariants of knots and 3-manifolds
Secondary: 57M50: Geometric structures on low-dimensional manifolds

braid transverse knots self-linking number


Kawamuro, Keiko; Pavelescu, Elena. The self-linking number in annulus and pants open book decompositions. Algebr. Geom. Topol. 11 (2011), no. 1, 553--585. doi:10.2140/agt.2011.11.553.

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