Algebraic & Geometric Topology 6 (2006) 1239–1265

DOI: 10.2140/agt.2006.6.1239

arXiv: math.GT/0601396

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 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.

Keywords

4–manifold, symplectic structure, Lefschetz fibration

Mathematical Subject Classification

Primary: 57M50, 57R17

Secondary: 57N13

References

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Publication

Received: 13 May 2006
Accepted: 26 June 2006
Published: 11 September 2006

Authors