We provide unipotent factorizations of vector bundle automorphisms of real and complex vector bundles over finite dimensional locally finite CW-complexes. This generalizes work of Thurston–Vaserstein and Vaserstein 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.

中文翻译：

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向量丛自同构的单能分解

我们提供了有限维局部有限 CW 复数上实数和复数向量丛的向量丛自同构的单能分解。这概括了 Thurston-Vaserstein 和 Vaserstein 对平凡向量丛的工作。我们还解决了两个辛案例，并提出了在 Stein 流形上设置全纯向量丛的问题的复杂几何模拟。