The Stacey-Roberts Lemma for Banach Manifolds
The Stacey-Roberts lemma states that a surjective submersion between finite-dimensional manifolds induces a submersion of smooth mappings on infinite-dimensional manifolds by pushforward. This result is foundational for many constructions in infinite-dimensional differential geometry, such as the co...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2025 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2025
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/213178 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | The Stacey-Roberts Lemma for Banach Manifolds. Peter Kristel and Alexander Schmeding. SIGMA 21 (2025), 037, 20 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | The Stacey-Roberts lemma states that a surjective submersion between finite-dimensional manifolds induces a submersion of smooth mappings on infinite-dimensional manifolds 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 that 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.
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| ISSN: | 1815-0659 |