Stein-fillable open books of genus one that do not admit positive factorisations
arXiv:2103.13250 · doi:10.4310/MRL.2023.v30.n3.a4
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.
8 pages, 6 figures