Kahler decomposition of 4-manifolds

Abstract

In this article we show that every closed oriented smooth 4-manifold can be decomposed into two codimension zero submanifolds (one with reversed orientation) so that both pieces are exact Kahler manifolds with strictly pseudoconvex boundaries and that induced contact structures on the common boundary are isotopic. Meanwhile, matching pairs of Lefschetz fibrations with bounded fibers are offered as the geometric counterpart of these structures. We also provide a simple topological proof of the existence of folded symplectic forms on 4-manifolds.

This is the version published by Algebraic & Geometric Topology on 11 September 2006

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Cited by in corpus (9)

• Constructing Lefschetz-type fibrations on four-manifolds
• Examples and counter-examples of log-symplectic manifolds
• Almost contact 5-folds are contact
• Constructions of contact forms on products and piecewise fibered manifolds
• Geometric structures and Lie algebroids
• Symplectic Origami
• Fibrations in semi-toric and generalized complex geometry
• Pseudo-holomorphic maps into folded symplectic four-manifolds
• Folded symplectic forms in contact topology