A Convex decomposition theorem for four-manifolds

Selman Akbulut; Rostislav Matveyev

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A Convex decomposition theorem for four-manifolds

Selman Akbulut·Rostislav Matveyev

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Abstract

We show that every smooth closed oriented four-manifold admits a decomposition into two co- dimension zero submanifolds with common boundary. Each of these submanifolds carries a structure of a symplectic manifold with pseudo-convex boundary. This imply, in particular, that every smooth closed simply-connected four-manifold is a Stein domain in the the complement of a certain contractible 2-complex.

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Selman Akbulut, Rostislav Matveyev. 2000-10-16. A Convex decomposition theorem for four-manifolds. https://arxiv.org/abs/math/0010166

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