Stein fillable manifolds and stably complex homotopy spheres

Diarmuid Crowley (University of Aberdeen)

Wednesday 22nd October, 2014 16:30-17:30 Maths 516


An almost contact structure on a (2q+1)-manifold M is a reduction of its structure group of M to unitary group U(q).  A special class of almost contact structure arise when M is the boundary of a Stein domain.

I this talk I will show how Eliashberg's h-principle for Stein domains leads to a bordism-theoretic characterisation of Stein fillable almost contact manifolds.  

As an example, I report on a new theorem that the (8k-1)-sphere admits non-Stein fillable almost contact structures so long as k > 1.  The proof uses on a number theoretic result about Bernoulli numbers.

This work is joint with Jonathan Bowden and Andras Stipsicz and Bernd Kellner.

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