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Constructing symplectic forms on 4–manifolds which vanish on circles
2004
Geometry and Topology
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Given a smooth, closed, oriented 4-manifold X and alpha in H_2(X,Z) such that alpha.alpha > 0, a closed 2-form w is constructed, Poincare dual to alpha, which is symplectic on the complement of a finite set of unknotted circles. The number of circles, counted with sign, is given by d = (c_1(s)^2 -3sigma(X) -2chi(X))/4, where s is a certain spin^C structure naturally associated to w.
doi:10.2140/gt.2004.8.743
fatcat:nxflinxry5eb5cdia3yf3ldhl4