Morse theory in definably complete d-minimal structures
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914924912967680 |
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| author | Fujita, Masato Kawakami, Tomohiro |
| author_facet | Fujita, Masato Kawakami, Tomohiro |
| contents | Consider a definable complete d-minimal expansion $(F, <, +, \cdot, 0, 1, \dots,)$ of an oredered field $F$. Let $X$ be a definably compact definably normal definable $C^r$ manifold and $2 \le r <\infty$. We prove that the set of definable Morse functions is open and dense in the set of definable $C^r$ functions on $X$ with respect to the definable $C^2$ topology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14675 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Morse theory in definably complete d-minimal structures Fujita, Masato Kawakami, Tomohiro Logic 03C64 Consider a definable complete d-minimal expansion $(F, <, +, \cdot, 0, 1, \dots,)$ of an oredered field $F$. Let $X$ be a definably compact definably normal definable $C^r$ manifold and $2 \le r <\infty$. We prove that the set of definable Morse functions is open and dense in the set of definable $C^r$ functions on $X$ with respect to the definable $C^2$ topology. |
| title | Morse theory in definably complete d-minimal structures |
| topic | Logic 03C64 |
| url | https://arxiv.org/abs/2408.14675 |