Title: On the Invariance of the Real Milnor Number

Speaker: Raphael de Omena Marinho (UNEAL, Brazil)

Abstract: The Milnor number is a classical topological invariant for complex singularities, but its behavior under real equivalences is much more subtle. In this talk, we present three new invariance results for the real Milnor number of smooth and real analytic function germs. First, we show that it is preserved under right-bi-Lipschitz equivalence, provided the initial parts of the germs have algebraically isolated singularities. We also show that it is invariant under right-C^1 equivalence under a similar condition on the initial part. Finally, we prove that the Milnor number is an invariant of the zero-set for irreducible real analytic germs. Sharpness examples for our conditions will also be discussed.

This is joint work with Edson Sampaio (UFC) and Emanoel Souza (UECE).