The topology of Stein fillable manifolds in high dimensions I

Abstract

We give a bordism-theoretic characterisation of those closed almost contact (2q+1)-manifolds (with q > 2) which admit a Stein fillable contact structure. Our method is to apply Eliashberg's h-principle for Stein manifolds in the setting of Kreck's modified surgery. As an application, we show that any simply connected almost contact 7-manifold with torsion free second homotopy group is Stein fillable. We also discuss the Stein fillability of exotic spheres and examine subcritical Stein fillability.

39 pages, more explanation added. To appear in Proc. London Math. Soc

References in corpus (1)

• The topology of Stein fillable manifolds in high dimensions II

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