Aldicio José Miranda (Universidade Federal de Uberlândia)

Thursday, Novmber 16th, 10:20, Room 4-111

**Title: Good real deformations of co-rank one map germs from $\R^3$ to $\R^3$.**

**Abstract:**

A stable perturbation of a finitely determined real map-germ from $(\R^n, S)$ to $(\R^{n+1}, 0)$ is called a {\it good real perturbation} if the inclusion of real image in complex image induces an isomorphism on $H_n$). The existence of good real deformations is an open question with partial answers for low dimensions and in special cases. The same question is also open for map germs from $(R^n, S)$ to $(R^p, 0)$ with $n \geq p$, with {\it discriminant} replacing {\it image} and $ \mu_{(\Delta)}$(Discriminant Milnor number) replacing $\mu_I$.

In this work we study the good real deformations of co-rank one map germs from $\R^3$ to $\R^3$. To obtain these results we give a full description of the topology of the discriminant of all real stable deformations of the germ.