 
Summary: arXiv:math.GT/001016616Oct2000
A CONVEX DECOMPOSITION THEOREM FOR
FOURMANIFOLDS
S. AKBULUT AND R. MATVEYEV
Abstract. In this article we show that every smooth closed oriented four
manifold admits a decomposition into two submanifolds along common bound
ary. Each of these submanifolds is a complex manifold with pseudoconvex
boundary. This imply, in particular, that every smooth closed simplyconnected
fourmanifold is a Stein domain in the the complement of a certain contractible
2complex.
1. Introduction
Exact manifold with pseudoconvex boundary (PC manifold, for short) is a com
pact complex manifold X, which admits strictly plurisubharmonic Morse function
, such that set of maximum points of coincides with the boundary X. We
prefer the term PC manifold, since combination of words "compact Stein manifold"
is likely to precipitate heart palpitations in some mathematicians.
Such manifold admits a symplectic structure = i
2 and serves as an analogue
of closed symplectic manifold. Boundary X of PC manifold X inherits a contact
structure , which, in this case, is a distribution of maximal complex subspaces in
