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
Datum:2025
Hauptverfasser: Kristel, Peter, Schmeding, Alexander
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2025
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

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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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.
ISSN:1815-0659