Unstability problem of real analytic maps
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866929505583497216 |
|---|---|
| author | Bekka, Karim Koike, Satoshi Ohmoto, Toru Shiota, Masahiro Tanabe, Masato |
| author_facet | Bekka, Karim Koike, Satoshi Ohmoto, Toru Shiota, Masahiro Tanabe, Masato |
| contents | As well-known, the $C^\infty$ stability of proper $C^\infty$ maps is characterized by the infinitesimal $C^\infty$ stability. In the present paper we study the counterpart in real analytic context. In particular, we show that the infinitesimal $C^ω$ stability does not imply $C^ω$ stability; for instance, a Whitney umbrella $\mathbb{R}^2 \to \mathbb{R}^3$ is not $C^ω$ stable. A main tool for the proof is a relative version of Whitney's Analytic Approximation Theorem which is shown by using H. Cartan's Theorems A and B. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18106 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unstability problem of real analytic maps Bekka, Karim Koike, Satoshi Ohmoto, Toru Shiota, Masahiro Tanabe, Masato Algebraic Geometry Geometric Topology 58K20, 57R45 As well-known, the $C^\infty$ stability of proper $C^\infty$ maps is characterized by the infinitesimal $C^\infty$ stability. In the present paper we study the counterpart in real analytic context. In particular, we show that the infinitesimal $C^ω$ stability does not imply $C^ω$ stability; for instance, a Whitney umbrella $\mathbb{R}^2 \to \mathbb{R}^3$ is not $C^ω$ stable. A main tool for the proof is a relative version of Whitney's Analytic Approximation Theorem which is shown by using H. Cartan's Theorems A and B. |
| title | Unstability problem of real analytic maps |
| topic | Algebraic Geometry Geometric Topology 58K20, 57R45 |
| url | https://arxiv.org/abs/2406.18106 |