Holomorphic Factorization of Mappings into $ \operatorname{Sp}_{4}( \mathbb{C}) $

Abstract

We prove that any null-homotopic holomorphic map from a Stein space $X$ to the symplectic group $\operatorname{Sp}_{4}(\mathbb{C})$ can be written as a finite product of elementary symplectic matrices with holomorphic entries.