Geodesic
Some notes on the local topology of a deformation of a function-germ with a one-dimensional critical set
Journal of Singularities, Tome 25 (2022), pp. 403-421

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The Brasselet number of a function f with nonisolated singularities describes numerically the topological information of its generalized Milnor fibre. In this work, we consider two function-germs f and g on a complex analytic space X such that f has a stratified isolated singularity at the origin and g has a stratified one-dimensional critical set. We use the Brasselet number to study the local topology of a deformation of g defined by adding a large power of f. As an application of this study, we present a new proof of the Lê-Yomdin formula for the Brasselet number. 
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     author = {Hellen Santana},
     title = {Some notes on the local topology of a deformation of a function-germ with a one-dimensional critical set},
     journal = {Journal of Singularities},
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Hellen Santana. Some notes on the local topology of a deformation of a function-germ with a one-dimensional critical set. Journal of Singularities, Tome 25 (2022), pp. 403-421. doi: 10.5427/jsing.2022.25t

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