Families of contact 3-manifolds with arbitrarily large Stein fillings

R. Inanc Baykur; Jeremy Van Horn-Morris

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arXiv · 1208.0528

Families of contact 3-manifolds with arbitrarily large Stein fillings

R. Inanc Baykur·Jeremy Van Horn-Morris

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Abstract

We show that there are vast families of contact 3-manifolds each member of which admits infinitely many Stein fillings with arbitrarily big euler characteristics and arbitrarily small signatures ---which disproves a conjecture of Stipsicz and Ozbagci. To produce our examples, we set a framework which generalizes the construction of Stein structures on allowable Lefschetz fibrations over the 2-disk to those over any orientable base surface, along with the construction of contact structures via open books on 3-manifolds to spinal open books introduced in [24].

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R. Inanc Baykur, Jeremy Van Horn-Morris. 2012-08-02. Families of contact 3-manifolds with arbitrarily large Stein fillings. https://arxiv.org/abs/1208.0528

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