Some notes on the local topology of a deformation of a function-germ with a one-dimensional critical set
Hellen Santana
Journal of Singularities
volume 25 (2022), 403-421
Received: 21 January 2021. Received in revised form: 8 March 2021.
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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, 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.
Key words and phrases:
Brasselet number, Euler obstruction, Milnor fibre, Lê-Yomdin formulas
Author(s) information:
Hellen Monção de Carvalho Santana
Universidade de São Paulo
Instituto de Ciências Matemáticas e de
Computação - USP
Avenida Trabalhador São-Carlense
400 - Centro, São Carlos, Brazil
hellenmcarvalho@hotmail.com
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