https://hal.inria.fr/hal-02912322Grigoriev, DimaDimaGrigorievLPP - Laboratoire Paul PainlevĂ© - UMR 8524 - UniversitĂ© de Lille - CNRS - Centre National de la Recherche ScientifiqueRadchenko, DanyloDanyloRadchenkoMPIM - Max Planck Institute for Mathematics - Max-Planck-GesellschaftON A TROPICAL VERSION OF THE JACOBIAN CONJECTUREHAL CCSD2019[INFO] Computer Science [cs][INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG]Monteil, Alain2020-08-05 16:14:252022-03-23 15:50:092020-08-05 16:14:52enConference papersapplication/pdf1We prove that, for a tropical rational map if for any point theconvex hull of Jacobian matrices at smooth points in a neighborhood of thepoint does not contain singular matrices then the map is an isomorphism. Wealso show that a tropical polynomial map on the plane is an isomorphism ifall the Jacobians have the same sign (positive or negative). In addition, for atropical rational map we prove that if the Jacobians have the same sign andif its preimage is a singleton at least at one regular point then the map is anisomorphism.