Algebraic & Geometric Topology

Kähler decomposition of 4–manifolds

R Inanç Baykur

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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.

Article information

Algebr. Geom. Topol., Volume 6, Number 3 (2006), 1239-1265.

Received: 13 May 2006
Accepted: 26 June 2006
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R17: Symplectic and contact topology 57M50: Geometric structures on low-dimensional manifolds
Secondary: 57N13: Topology of $E^4$ , $4$-manifolds [See also 14Jxx, 32Jxx]

4–manifold symplectic structure Lefschetz fibration


Baykur, R Inanç. Kähler decomposition of 4–manifolds. Algebr. Geom. Topol. 6 (2006), no. 3, 1239--1265. doi:10.2140/agt.2006.6.1239.

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