In this note we give a simple proof of the following relative analog of the well known Milnor-Palamodov theorem: the Bruce-Roberts number of a function relative to an isolated hypersurface singularity is equal to its topological Milnor number (the rank of a certain relative (co)homology group) if and only if the hypersurface singularity is quasihomogeneous. The proof relies on an interpretation of the Bruce-Roberts number in terms of differential forms and the Lê-Greuel formula.

中文翻译：

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孤立超曲面奇点函数的米尔诺-帕拉莫多夫定理

在这篇笔记中，我们给出了众所周知的 Milnor-Palamodov 定理的以下相对类比的简单证明：一个函数相对于孤立的超曲面奇点的 Bruce-Roberts 数等于它的拓扑米尔诺数（某个相对的等级(co)homology group) 当且仅当超曲面奇点是准齐次的。证明依赖于布鲁斯-罗伯茨数在微分形式和 Lê-Greuel 公式方面的解释。