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Holomorphic factorization of mappings into $\operatorname{Sp}_4(\mathbb{C})$

Björn Ivarsson, Frank Kutzschebauch and Erik Løw

Vol. 16 (2023), No. 1, 233–277
Abstract

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

Keywords
Oka principle, Stein spaces, symplectic matrices, unipotent factorization, elementary symplectic matrices, rings of holomorphic functions, algebraic K-theory
Mathematical Subject Classification
Primary: 32Q56
Secondary: 19B14
Milestones
Received: 28 May 2020
Revised: 8 May 2021
Accepted: 10 June 2021
Published: 14 April 2023
Authors
Björn Ivarsson
Department of Mathematics and Systems Analysis
Aalto University
Aalto
Finland
Frank Kutzschebauch
Departement Mathematik
Universität Bern
Bern
Switzerland
Erik Løw
Department of Mathematics
University of Oslo
Oslo
Norway

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