A Convex decomposition theorem for four-manifolds

2000/10/16 by Selman Akbulut, Rostislav Matveyev
Mathematics · #math.GT #math.SG #msc:57M50 #msc:57R17

paper · pdf

published as Internat. Math. Res. Notices 1998, no. 7, 371--381 · LaTeX2e, 9 pages, 5 figures

arxiv created 2000/10/16 · arxiv updated 2009/11/30

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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