1. Unstability problem of real analytic maps
- Author
-
Bekka, Karim, Koike, Satoshi, Ohmoto, Toru, Shiota, Masahiro, and Tanabe, Masato
- Subjects
Mathematics - Algebraic Geometry ,Mathematics - Geometric Topology ,58K20, 57R45 - Abstract
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 $C^\omega$ stability does not imply $C^\omega$ stability; for instance, a Whitney umbrella $\mathbb{R}^2 \to \mathbb{R}^3$ is not $C^\omega$ 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., Comment: 7 pages
- Published
- 2024