Kahler decomposition of 4-manifolds

Details Kahler decomposition of 4-manifolds Kahler decomposition of 4-manifolds

2006-01-17

arxiv.org/abs/math/0601396v3

Algebr. Geom. Topol. 6 (2006) 1239-1265

Mathematics

Geometric Topology

This is the version published by Algebraic & Geometric Topology on 11 September 2006

Scientific paper

10.2140/agt.2006.6.1239

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 Kahler 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.

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