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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.03366 |
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| _version_ | 1866915529978019840 |
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| author | Pinaud, Matthieu F. |
| author_facet | Pinaud, Matthieu F. |
| contents | Let $M$ be a compact smooth manifold with corners and $N$ be a finite dimensional smooth manifold without boundary which admits local addition. We define a smooth manifold structure to general sets of continuous mapings $\mathcal{F}(M,N)$ whenever functions spaces $\mathcal{F}(U,\mathbb{R})$ on open subsets $U\subseteq [0,\infty)^n$ are given, subject to simple axioms. Construction and properties of spaces of sections and smoothness of natural mappings between spaces $\mathcal{F}(M,N)$ are discussed, like superposition operators $\mathcal{F}(M,f):\mathcal{F}(M,N_1)\to \mathcal{F}(M,N_2)$, $η\mapsto f\circ η$ for smooth maps $f:N_1\to N_2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_03366 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Manifolds of mappings associated with real-valued function spaces and natural mappings between them Pinaud, Matthieu F. Differential Geometry Let $M$ be a compact smooth manifold with corners and $N$ be a finite dimensional smooth manifold without boundary which admits local addition. We define a smooth manifold structure to general sets of continuous mapings $\mathcal{F}(M,N)$ whenever functions spaces $\mathcal{F}(U,\mathbb{R})$ on open subsets $U\subseteq [0,\infty)^n$ are given, subject to simple axioms. Construction and properties of spaces of sections and smoothness of natural mappings between spaces $\mathcal{F}(M,N)$ are discussed, like superposition operators $\mathcal{F}(M,f):\mathcal{F}(M,N_1)\to \mathcal{F}(M,N_2)$, $η\mapsto f\circ η$ for smooth maps $f:N_1\to N_2$. |
| title | Manifolds of mappings associated with real-valued function spaces and natural mappings between them |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2506.03366 |