## 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

#### Jagiellonian University, Poland   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloakf78ce06fbefa3bb68673b92369e5089e').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addyf78ce06fbefa3bb68673b92369e5089e = '&#97;nn&#97;.v&#97;l&#101;tt&#101;' + '&#64;'; addyf78ce06fbefa3bb68673b92369e5089e = addyf78ce06fbefa3bb68673b92369e5089e + '&#105;m' + '&#46;' + '&#117;j' + '&#46;' + '&#101;d&#117;' + '&#46;' + 'pl'; var addy_textf78ce06fbefa3bb68673b92369e5089e = '&#97;nn&#97;.v&#97;l&#101;tt&#101;' + '&#64;' + '&#105;m' + '&#46;' + '&#117;j' + '&#46;' + '&#101;d&#117;' + '&#46;' + 'pl';document.getElementById('cloakf78ce06fbefa3bb68673b92369e5089e').innerHTML += '<a ' + path + '\'' + prefix + ':' + addyf78ce06fbefa3bb68673b92369e5089e + '\'>'+addy_textf78ce06fbefa3bb68673b92369e5089e+'<\/a>';

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.