Local Properties of Self-Dual Harmonic 2-forms on a 4-Manifold
نویسنده
چکیده
We will prove a Moser-type theorem for self-dual harmonic 2-forms on closed 4manifolds, 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 S1×S2, after a slight modification, must be one of two possibilities.
منابع مشابه
Seiberg–Witten Invariants and Pseudo-Holomorphic Subvarieties for Self-Dual, Harmonic 2–Forms
A smooth, compact 4–manifold with a Riemannian metric and b2+ ≥ 1 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...
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تاریخ انتشار 1997