The topology of Stein fillable manifolds in high dimensions i

Jonathan Bowden, Diarmuid Crowley, András I. Stipsicz

Research output: Contribution to journalArticleResearchpeer-review

10 Citations (Scopus)


We give a bordism-theoretic characterization of those closed almost contact (2q+1)-manifolds (with q≥2) that 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.

Original languageEnglish
Pages (from-to)1363-1401
Number of pages39
JournalProceedings of the London Mathematical Society
Issue number6
Publication statusPublished - 2014
Externally publishedYes

Cite this