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.