## View abstract

### Session S14 - Global Injectivity, Jacobian Conjecture, and Related Topics

Wednesday, July 14, 12:50 ~ 13:40 UTC-3

## Jacobian conjecture via intersection homology

### Anna Valette

The aim of this talk is to give an approach to the Jacobian conjecture using intersection homology. The main idea is to reduce the study of a given mapping $F:\mathbb{C}^n \to \mathbb{C}^n$ to the study of a singular semi-algebraic set. We will construct a pseudomanifold $N_F$ (i.e. a semi-algebraic subset of $\mathbb{R}^m$ whose singular locus is of codimension at least $2$ in itself and whose regular locus is dense in itself) associated to a given polynomial map $F:\mathbb{C}^n\to\mathbb{C}^n$. We will show that in the case $n=2$, the map $F$ with non-vanishing Jacobian is not proper iff the intersection homology of $N_F$ is nontrivial.