Unipotent Factorization of Vector Bundle Automorphisms

TL;DR

This paper develops a unipotent factorization framework for automorphisms of vector bundles over manifolds, extending previous results and exploring symplectic and complex geometric cases.

Contribution

It generalizes unipotent factorization methods to non-trivial vector bundles and introduces new approaches for symplectic and holomorphic bundles.

Findings

Unipotent factorizations are possible for real and complex vector bundle automorphisms.

Extension of factorization techniques to symplectic vector bundles.

Proposal of a complex geometric analog for holomorphic vector bundles over Stein manifolds.

Abstract

We provide unipotent factorizations of vector bundle automorphisms of real and complex vector bundles over smooth manifolds. This generalises work of Thurston-Wasserstein and Wasserstein for trivial vector bundles. We also address two symplectic cases and propose a complex geometric analog of the problem in the setting of holomorphic vector bundles over Stein manifolds.