The Stacey-Roberts Lemma for Banach Manifolds
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916740994170880 |
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| author | Kristel, Peter Schmeding, Alexander |
| author_facet | Kristel, Peter Schmeding, Alexander |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00587 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Stacey-Roberts Lemma for Banach Manifolds Kristel, Peter Schmeding, Alexander Differential Geometry 58D15 (Primary), 58B20, 58B10, 53C05 (Secondary) 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. |
| title | The Stacey-Roberts Lemma for Banach Manifolds |
| topic | Differential Geometry 58D15 (Primary), 58B20, 58B10, 53C05 (Secondary) |
| url | https://arxiv.org/abs/2411.00587 |