A proof of a theorem of Luttinger and Simpson about the number of vanishing circles of a near-symplectic form on a 4-dimensional manifold

A proof is given of a theorem announced some years ago by Luttinger and Simpson to the effect that a compact 4-manifold that has a near-symplectic form in a given cohomology class admits one in the same class whose zero locus consists of any given, but strictly positive number of disjoint, embedded circles.

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Published 1 January 2006