Flows and Homotopies of Banach Lie algebroids

@misc{pelletier2026flows,
  title = {{Flows and Homotopies of Banach Lie algebroids}},
  author = {Fernand Pelletier and Alexander Schmeding},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.28148},
  eprint = {2608.28148},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.28148},
}

TY  - UNPB
TI  - Flows and Homotopies of Banach Lie algebroids
AU  - Fernand Pelletier
AU  - Alexander Schmeding
PY  - 2026
DA  - 2026/08/28
PB  - arXiv
DO  - 10.48550/arxiv.2608.28148
UR  - https://arxiv.org/abs/2608.28148
AB  - 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.
ER  -