关于形变强双Lipschitz平凡性
On Strong Bi-Lipschitz Triviality of Deformations
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中文总结 AI 辅助
本文通过构造反例，证明Thom-Levine判据的逆命题在双Lipschitz范畴不成立，即存在双Lipschitz平凡但非强双Lipschitz平凡的形变。
中文摘要 AI 辅助
Thom-Levine定理是一种经典方法，通过积分合适的向量场来证明形变的平凡性。在本文中，我们表明该判据的逆命题在双Lipschitz范畴内不成立。更确切地说，我们给出了一个二元实函数芽的光滑单参数形变的例子，该形变是双Lipschitz平凡的，但不是强双Lipschitz平凡的。中心芽具有孤立临界点，尽管它不是有限确定的。
英文摘要
The Thom-Levine theorem is a classical method for proving the triviality of deformations by integrating suitable vector fields. In this note, we show that the converse of this criterion does not hold in the bi-Lipschitz category. More precisely, we give an example of a smooth one-parameter deformation of a real function germ in two variables which is bi-Lipschitz trivial but not strongly bi-Lipschitz trivial. The central germ has an isolated critical point, though it is not finitely determined.
发表机构
- Indian Institute of Technology Goa（印度果阿理工学院）
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