A remark on $\mathscr{C}^\infty$ definable equivalence
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866911845664686080 |
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| author | Valette, Anna Valette, Guillaume |
| author_facet | Valette, Anna Valette, Guillaume |
| contents | We establish that if a submanifold $M$ of $\mathbb{R}^n$ is definable in some o-minimal structure then any definable submanifold $N\subset \mathbb{R}^n$ which is $\mathscr{C}^\infty$ diffeomorphic to $M$, with a diffeomorphism $h:N\to M$ that is sufficiently close to the identity, must be $\mathscr{C}^\infty$ definably diffeomorphic to $M$. The definable diffeomorphism between $N$ and $M$ is then provided by a tubular neighborhood of $M$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03164 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A remark on $\mathscr{C}^\infty$ definable equivalence Valette, Anna Valette, Guillaume Algebraic Geometry Logic 32B20, 58C25, 03C64 We establish that if a submanifold $M$ of $\mathbb{R}^n$ is definable in some o-minimal structure then any definable submanifold $N\subset \mathbb{R}^n$ which is $\mathscr{C}^\infty$ diffeomorphic to $M$, with a diffeomorphism $h:N\to M$ that is sufficiently close to the identity, must be $\mathscr{C}^\infty$ definably diffeomorphic to $M$. The definable diffeomorphism between $N$ and $M$ is then provided by a tubular neighborhood of $M$. |
| title | A remark on $\mathscr{C}^\infty$ definable equivalence |
| topic | Algebraic Geometry Logic 32B20, 58C25, 03C64 |
| url | https://arxiv.org/abs/2403.03164 |