Abstract

We consider the topological classification of finitely determined map germs $f:(\mathbb {R}^n,0)\to (\mathbb {R}^p,0)$ with $f^{-1}(0)\neq \{0\}$. Associated with $f$ we have a link diagram, which is well defined up to topological equivalence. We prove that $f$ is topologically $\mathcal {A}$-equivalent to the generalized cone of its link diagram.

中文翻译：

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锥体结构定理

摘要

我们考虑有限确定的地图细菌的拓扑分类 $f:(\mathbb {R}^n,0)\to (\mathbb {R}^p,0)$ 与 $f^{-1}(0)\ neq \{0\}$。与 $f$ 相关联，我们有一个链接图，它被很好地定义为拓扑等价。我们证明 $f$ 在拓扑上 $\mathcal {A}$-等价于其链接图的广义锥。