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Abstract
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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 Kähler 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.
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Keywords
4–manifold, symplectic structure, Lefschetz fibration
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Mathematical Subject Classification 2000
Primary: 57R17, 57M50
Secondary: 57N13
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Publication
Received: 13 May 2006
Accepted: 26 June 2006
Published: 11 September 2006
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