Constructing symplectic forms on 4-manifolds which vanish on circles
Abstract
Given a smooth, closed, oriented 4-manifold X and alpha in H2(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 = (c1(s)2 -3sigma(X) -2chi(X))/4, where s is a certain spinC structure naturally associated to w.
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