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 |
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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 |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862619501994967040 |
|---|---|
| author | Kristel, Peter Schmeding, Alexander |
| author_facet | Kristel, Peter Schmeding, Alexander |
| citation_txt | The Stacey-Roberts Lemma for Banach Manifolds. Peter Kristel and Alexander Schmeding. SIGMA 21 (2025), 037, 20 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-03-21T11:59:15Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-213178 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T11:59:15Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kristel, Peter Schmeding, Alexander 2026-02-16T16:33:46Z 2025 The Stacey-Roberts Lemma for Banach Manifolds. Peter Kristel and Alexander Schmeding. SIGMA 21 (2025), 037, 20 pages 1815-0659 2020 Mathematics Subject Classification: 58D15; 58B20; 58B10; 53C05 arXiv:2411.00587 https://nasplib.isofts.kiev.ua/handle/123456789/213178 https://doi.org/10.3842/SIGMA.2025.037 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. The authors wish to thank P. Steffens, who brought the error in the published proof of the Stacey–Roberts lemma to their attention. We thank the referees for their diligent work, which led to numerous improvements to the manuscript. Dedicated to D.M. Roberts on the occasion of his 5th strong prime birthday. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Stacey-Roberts Lemma for Banach Manifolds Article published earlier |
| spellingShingle | The Stacey-Roberts Lemma for Banach Manifolds Kristel, Peter Schmeding, Alexander |
| title | The Stacey-Roberts Lemma for Banach Manifolds |
| title_full | The Stacey-Roberts Lemma for Banach Manifolds |
| title_fullStr | The Stacey-Roberts Lemma for Banach Manifolds |
| title_full_unstemmed | The Stacey-Roberts Lemma for Banach Manifolds |
| title_short | The Stacey-Roberts Lemma for Banach Manifolds |
| title_sort | stacey-roberts lemma for banach manifolds |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/213178 |
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