Volume 6, issue 3 (2006)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Kähler decomposition of 4–manifolds

R Inanç Baykur

Algebraic & Geometric Topology 6 (2006) 1239–1265

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 2000
Primary: 57R17, 57M50
Secondary: 57N13
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Publication
Received: 13 May 2006
Accepted: 26 June 2006
Published: 11 September 2006
Authors
R Inanç Baykur
Department of Mathematics
Michigan State University
East Lansing MI 48824
USA