Constructing symplectic forms on 4-manifolds which vanish on circles

Details Constructing symplectic forms on 4-manifolds which vanish on circles Constructing symplectic forms on 4-manifolds which vanish on circles

2004-01-15

arxiv.org/abs/math/0401186v2

Geom. Topol. 8(2004) 743-777

Mathematics

Geometric Topology

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper20.abs.html

Scientific paper

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.

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