2,428 research outputs found
Fibrations and contact structures
We prove that a closed 3-dimensional manifold is a torus bundle over the circle if and only if it carries a closed nonsingular 1-form which is linearly deformable into contact forms
Families of contact 3-manifolds with arbitrarily large Stein fillings
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].Comment: 36 pages, 9 figures, with an appendix by Samuel Lisi and Chris Wend
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