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

TL;DR

This paper proves that null-homotopic holomorphic maps from Stein spaces to the symplectic group Sp_4(C) can be decomposed into finite products of elementary matrices, advancing understanding of holomorphic factorizations in complex geometry.

Contribution

It establishes a holomorphic factorization result for maps into Sp_4(C), showing they can be expressed as finite products of elementary matrices, which was previously unknown.

Findings

Any null-homotopic holomorphic map from Stein space to Sp_4(C) can be factorized.

The factorization involves a finite product of elementary symplectic matrices.

The result applies to complex geometry and holomorphic mapping theory.

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.