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# Mathematical Research Letters

## Volume 13 (2006)

### Number 4

### 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

Pages: 557 – 570

DOI: http://dx.doi.org/10.4310/MRL.2006.v13.n4.a6

#### Author

#### Abstract

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.