Holomorphic factorization of mappings into $\mathrm{SL}_n(\mathbb{C})$

Abstract

We solve Gromov’s Vaserstein problem. Namely, we show that a null-homotopic holomorphic mapping from a finite dimensional reduced Stein space into $\mathrm{SL}_n(\mathbb{C})$ can be factored into a finite product of unipotent matrices with holomorphic entries.