The topology of Stein fillable manifolds in high dimensions, II

Jonathan Bowden, Diarmuid Crowley, András I. Stipsicz, Bernd C. Kellner

Research output: Contribution to journalArticle

4 Citations (Scopus)


We continue our study of contact structures on manifolds of dimension at least five using surgery-theoretic methods. Particular applications include the existence of “maximal” almost contact manifolds with respect to the Stein cobordism relation as well as the existence of weakly fillable contact structures on the product M * S2. We also study the connection between Stein fillability and connected sums: we give examples of almost contact manifolds for which the connected sum is Stein fillable, while the components are not. Concerning obstructions to Stein fillability, we show for all k > 1 that there are almost contact structures on the 8k-1/–sphere which are not Stein fillable. This implies the same result for all highly connected .8k-1/–manifolds which admit almost contact structures. The proofs rely on a new number-theoretic result about Bernoulli numbers.

Original languageEnglish
Pages (from-to)2995-3030
Number of pages36
JournalGeometry and Topology
Issue number5
Publication statusPublished - Oct 20 2015


  • Bordism theory
  • Contact structures
  • Stein fillability
  • Surgery

ASJC Scopus subject areas

  • Geometry and Topology

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