English

Constructing symplectic forms on 4-manifolds which vanish on circles

Geometric Topology 2014-11-11 v2 Differential Geometry Symplectic Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.math/0401186,
  title  = {Constructing symplectic forms on 4-manifolds which vanish on circles},
  author = {David T. Gay and Robion Kirby},
  journal= {arXiv preprint arXiv:math/0401186},
  year   = {2014}
}

Comments

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

R2 v1 2026-07-22T17:01:36.370Z