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arXiv · 1909.00803

Brasselet number and function-germs with a one-dimensional critical set

Hellen Santana
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Abstract

The Brasselet number of a function $f$ with nonisolated singularities describes numerically the topological information of its generalized Milnor fibre. In this work, using the Brasselet number, we present several formulas for germs $f:(X, 0) \rightarrow (\mathbb{C}, 0)$ and $g : (X, 0)\rightarrow (\mathbb{C}, 0)$ 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.

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Hellen Santana. 2019-09-02. Brasselet number and function-germs with a one-dimensional critical set. https://arxiv.org/abs/1909.00803

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