Algebraic & Geometric Topology

Kähler decomposition of 4–manifolds

R Inanç Baykur

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796576

Digital Object Identifier
doi:10.2140/agt.2006.6.1239

Mathematical Reviews number (MathSciNet)
MR2253445

Zentralblatt MATH identifier
1133.57011

Subjects
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]

Keywords
4–manifold symplectic structure Lefschetz fibration

Citation

Baykur, R Inanç. Kähler decomposition of 4–manifolds. Algebr. Geom. Topol. 6 (2006), no. 3, 1239--1265. doi:10.2140/agt.2006.6.1239. https://projecteuclid.org/euclid.agt/1513796576


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