**abstract:**
I will explain my recent construction of holomorphic functions without critical points on Stein manifolds. On open Riemann surfaces (which are precisely one dimensional Stein manifolds) such function were constructed in 1967 by Gunning and Narasimhan, but their proof does not extend to higher dimension. I will also give an almost precise answer to the question as to how many holomorphic functions with everywhere independent differentials do there exist on a given Stein manifold. The exposition will be complete and self contained.

<< Go back