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.

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Authors

Björn Ivarsson

Mathematisches Institut
Universität Bern
Sidlerstrasse 5
CH-3012 Bern
Switzerland

Frank Kutzschebauch

Mathematisches Institut
Universität Bern
Sidlerstrasse 5
CH-3012 Bern
Switzerland