AI 中文总结
本文针对巴拿赫李代数胚建立了不依赖紧支集延拓的流与同伦工具，构造了相关延拓、演化公式，证明了容许路径同伦的等价刻画，为其局部积分方案提供了理论基础。
AI 中文摘要
我们建立了不依赖紧支集延拓的巴拿赫李代数胚的流与同伦工具。在合适假设下，我们构造了沿代数胚路径的参数依赖的截面局部延拓、完全提升及其纤维线性演化，以及博赫纳积分形式的常数变易公式。随后我们证明，容许路径同伦等价于从参数正方形出发的李代数胚态射及相关传输方程的解。这为后续发展巴拿赫李代数胚局部积分方案提供了所需的延拓、传输与无穷小变分理论。
英文摘要
We establish flow and homotopy tools for Banach Lie algebroids that do not rely on compactly supported extensions. Under suitable hypotheses, we construct parameter-dependent local extensions of sections along algebroid paths, complete lifts and their fibrewise-linear evolutions, and a Bochner-integral variation-of-constants formula. We then prove that an admissible-path homotopy is equivalently a Lie algebroid morphism from the parameter square and a solution of the associated transport equation. This provides the extension, transport and infinitesimal variation theory required for a local integration program of Banach Lie algebroids to be developed in a sequel.
Comments40 pages, uses TikZ
