Mathematical Research Letters

Volume 30 (2023)

Number 3

Stein-fillable open books of genus one that do not admit positive factorisations

Pages: 709 – 719

DOI: https://dx.doi.org/10.4310/MRL.2023.v30.n3.a4

Authors

Vitalijs Brejevs (School of Mathematics and Statistics, University of Glasgow, United Kingdom)

Andy Wand (School of Mathematics and Statistics, University of Glasgow, United Kingdom)

Abstract

We construct an infinite family of genus one open book decompositions supporting Stein-fillable contact structures and show that their monodromies do not admit positive factorisations. This extends a line of counterexamples in higher genera and establishes that a correspondence between Stein fillings and positive factorisations only exists for planar open book decompositions.

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The first author was supported by the Carnegie Trust for the Universities of Scotland.

Received 5 May 2021

Received revised 5 March 2022

Accepted 21 March 2022

Published 15 December 2023