The Brasselet number of a function f hnonisolated singularities describes numerically the topological information of its generalized Milnor fibre. In this work, using the Brasselet number, we present several formulas for germs $$f:(X,0)\rightarrow (\mathbb {C},0)$$ f : ( X , 0 ) → ( C , 0 ) and $$g:(X,0)\rightarrow (\mathbb {C},0)$$ g : ( X , 0 ) → ( C , 0 ) in the case where g has a one-dimensional critical locus. We also give applications when f has isolated singularities and when it is a generic linear form.

中文翻译：

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Brasselet 数和功能-具有一维临界集的细菌

函数 f 非孤立奇点的 Brasselet 数在数值上描述了其广义 Milnor 纤维的拓扑信息。在这项工作中，使用 Brasselet 数，我们提出了几个细菌公式 $$f:(X,0)\rightarrow (\mathbb {C},0)$$ f : ( X , 0 ) → ( C , 0 )和 $$g:(X,0)\rightarrow (\mathbb {C},0)$$ g : ( X , 0 ) → ( C , 0 ) 在 g 具有一维临界轨迹的情况下。我们还给出了当 f 具有孤立的奇点并且它是通用线性形式时的应用。