Dimitri Grigoryev - On a Tropical Version of the Jacobian Conjecture
Channel: Institut des Hautes Études Scientifiques (IHÉS)
Date: 2021-02-04

We prove that, for a tropical rational map if for any point the convex hull of Jacobian matrices at smooth points in a neighborhood of the point does not contain singular matrices then the map is an isomorphism. We also show that a tropical polynomial map on the plane is an isomorphism if all the Jacobians have the same sign (positive or negative). In addition, for a tropical rational map we prove that if the Jacobians have the same sign and if its preimage is a singleton at least at one regular point then the map is an isomorphism. This is a joint work with Danylo Radchenko, ETH (Zürich).


Slides :
https://indico.math.cnrs.fr/event/6181/contributions/4948/attachments/2626/3328/tropical_jacobian_beamer.pdf