Faculty of Mathematics
Collaborative Research Centre 701
Spectral Structures and Topological Methods in Mathematics
stripes SFB701

Wednesday, July 03, 2013 - 14:15 in V4-112

The topology of Stein fillable manifolds in higher dimensions

A talk in the 'Seminar Geometrie-Topologie' series by
Diarmuid Crowley from Bonn
Abstract: An almost contact manifold M is a closed oriented (2q+1)-manifold with a reduction of its structure group to U(q). It is an open question in dimensions 7 and higher whether every almost contact manifold admits an actual contact structure. A special class of contact structure arise when M is the boundary of a Stein domain and Eliashberg's h-principle, a deep result in the subject, characterises Stein domains. I this talk I will report on joint work with Jonathan Bowden and Andras Stipsicz where we apply Eliashberg's h-principle in the setting of Kreck's modified surgery. As a consequence, we obtain a bordism-theoretic characterisation of which almost contact manifolds admit Stein fillings. As an application, we show that every simply connected almost contact 7-manifold with torsion free second integral homology admits a Stein filling.