Local Properties of Self-Dual Harmonic 2-forms on a 4-Manifold

Details Local Properties of Self-Dual Harmonic 2-forms on a 4-Manifold Local Properties of Self-Dual Harmonic 2-forms on a 4-Manifold

1997-05-30

arxiv.org/abs/dg-ga/9705010v2

Mathematics

Differential Geometry

9 pages, LaTex

Scientific paper

We will prove a Moser-type theorem for self-dual harmonic 2-forms on closed 4-manifolds, and use it to classify local forms on neighborhoods of singular circles on which the 2-form vanishes. Removing neighborhoods of the circles, we obtain a symplectic manifold with contact boundary - we show that the contact form on each S^1\times S^2, after a slight modification, must be one of two possibilities.

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