Seiberg-Witten invariants and pseudo-holomorphic subvarieties for self-dual, harmonic 2-forms
Symplectic Geometry
2014-11-11 v1 Geometric Topology
Abstract
A smooth, compact 4-manifold with a Riemannian metric and b^(2+) > 0 has a non-trivial, closed, self-dual 2-form. If the metric is generic, then the zero set of this form is a disjoint union of circles. On the complement of this zero set, the symplectic form and the metric define an almost complex structure; and the latter can be used to define pseudo-holomorphic submanifolds and subvarieties. The main theorem in this paper asserts that if the 4-manifold has a non zero Seiberg-Witten invariant, then the zero set of any given self-dual harmonic 2-form is the boundary of a pseudo-holomorphic subvariety in its complement.
Cite
@article{arxiv.math/9907199,
title = {Seiberg-Witten invariants and pseudo-holomorphic subvarieties for self-dual, harmonic 2-forms},
author = {Clifford Henry Taubes},
journal= {arXiv preprint arXiv:math/9907199},
year = {2014}
}
Comments
44 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol3/paper8.abs.html