The Stacey-Roberts Lemma for Banach Manifolds
Differential Geometry
2025-05-20 v3
Abstract
The Stacey-Roberts lemma states that a surjective submersion between finite-dimensional manifolds gives rise to a submersion on infinite-dimensional manifolds of smooth mappings by pushforward. This result is foundational for many constructions in infinite-dimensional differential geometry such as the construction of Lie groupoids of smooth mappings. We generalise the Stacey-Roberts lemma to Banach manifolds which admit smooth partitions of unity.The new approach also remedies an error in the original proof of the result for the purely finite-dimensional setting.
Keywords
Cite
@article{arxiv.2411.00587,
title = {The Stacey-Roberts Lemma for Banach Manifolds},
author = {Peter Kristel and Alexander Schmeding},
journal= {arXiv preprint arXiv:2411.00587},
year = {2025}
}