Stein Structures: Existence and Flexibility

Stein Structures: Existence and Flexibility - Kai Cieliebak

Kai Cieliebak
Ludwig-Maximilians-Universitat, Munich, Germany
February 29, 2012

This is a series of 3 talks on the topology of Stein manifolds, based on work of Eliashberg since the early 1990ies. More specifically, I wish to explain to what extent Stein structures are flexible, i.e. obey an h-principle. After providing some general background on Stein manifolds, the first talk will focus on the construction of plurisubharmonic functions with specific properties. Using these, I will in the second talk present the proof of Eliashberg's existence theorem for Stein structures.
The third talk concerns several flexibility results: an h-cobordism theorem for Stein structures, realization of pseudo-isotopies by Stein structures, and a new class of "flexible Stein structures" that obey a 1-parametric h-principle.