Hellen Santana

Wednesday, October 21st, 2020. Gmeet at 4:20 pm

Title: Lê-Iomdine formula for the Brasselet number

Abstract: Let $f, g : (X, 0)\rightarrow (\mathbb{C}, 0)$ be germs of analytic functions
defined over a complex analytic space $X$. The Brasselet number of a function $f$
describes numerically the topology of its generalized Milnor fibre. We study the local
topology of a deformation of $g, \ \tilde{g}=g+f^N,$ for a positive integer number
$N\gg1$ and provide a relation between the Brasselet number of $g$ and $\tilde{g}$
in $X\cap\{f=0\}$, in the case where $f$ has isolated singularity at the origin.