Kähler decomposition of 4–manifolds

Baykur, R Inanç

doi:10.2140/agt.2006.6.1239

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Kähler decomposition of 4–manifolds

R Inanç Baykur

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 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

Volume 6, issue 3 (2006)