Northern California Symplectic Geometry Seminar: H-principle for complex contact structures on Stein manifolds

Seminar | February 4 | 4-5 p.m. | 740 Evans Hall

 Franc Forstneric, University of Ljublana

 Department of Mathematics

The aim of this talk is to present a first attempt towards homotopy classification of holomorphic contact structures on Stein manifolds. We introduce the notion of a formal complex contact structure and show that any such structure on an odd dimensional Stein manifold $X$ is homotopic (through formal contact structures) to a genuine holomorphic contact structure on a Stein domain in X which is diffeotopic to $X$. The parametric h-principle also holds in this setting. On Stein threefolds we have a complete homotopy classification of formal complex contact structures. It is currently not understood whether these holomorphic contact structures could be realized on the whole Stein manifold $X$.