Seiberg-Witten invariants and pseudo-holomorphic subvarieties for self-dual, harmonic 2-forms

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.

44 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol3/paper8.abs.html

References in corpus (2)

• Circle-valued Morse theory and Reidemeister torsion
• The structure of pseudo-holomorphic subvarieties for a degenerate almost complex structure and symplectic form on S^1 X B^3

Cited by in corpus (6)

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• Lagrangian matching invariants for fibred four-manifolds: II
• The structure of pseudo-holomorphic subvarieties for a degenerate almost complex structure and symplectic form on S^1 X B^3
• A compendium of pseudoholomorphic beasts in R x (S^1 x S^2)
• Taming the pseudoholomorphic beasts in $\mathbb{R}\times (S^1\times S^2)$
• Poisson structures of near-symplectic manifolds and their cohomology