Monopoles and contact 3-manifolds

Mathematics – Differential Geometry

Scientific paper

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25pages

Scientific paper

We propose the study of some kind of monopole equations directly associated
with a contact structure. Through a rudimentary analysis about the solutions,
we show that a closed contact 3-manifold with positive Tanaka-Webster curvature
and vanishing torsion must be either not symplectically semifillable or having
torsion Euler class of the contact structure.

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