## View abstract

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

Tuesday, July 20, 18:00 ~ 18:50 UTC-3

## A counterexample to a conjecture of Nollet and Xavier

### Jean Venato-Santos

#### Universidade Federal de Uberlândia, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloakc83a277efaa7f9aa92b6b6d3700f0b73').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addyc83a277efaa7f9aa92b6b6d3700f0b73 = 'jv&#101;n&#97;t&#111;s' + '&#64;'; addyc83a277efaa7f9aa92b6b6d3700f0b73 = addyc83a277efaa7f9aa92b6b6d3700f0b73 + 'gm&#97;&#105;l' + '&#46;' + 'c&#111;m'; var addy_textc83a277efaa7f9aa92b6b6d3700f0b73 = 'jv&#101;n&#97;t&#111;s' + '&#64;' + 'gm&#97;&#105;l' + '&#46;' + 'c&#111;m';document.getElementById('cloakc83a277efaa7f9aa92b6b6d3700f0b73').innerHTML += '<a ' + path + '\'' + prefix + ':' + addyc83a277efaa7f9aa92b6b6d3700f0b73 + '\'>'+addy_textc83a277efaa7f9aa92b6b6d3700f0b73+'<\/a>';

In this lecture we present a non-injective analytic local diffeomorphism of $\mathbb{R}^3$ such that the pre-image of every affine hyperplane is connected. This disproves a conjecture proposed by S. Nollet and F. Xavier in 2002. The talk is based on collaborations with F. Braun from Universidade Federal de São Carlos and L.R.G. Dias from Universidade Federal de Uberlândia.