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

2019/09/02 by Santana, Hellen
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1909.00803

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) → (ℂ, 0) and 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.

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