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).
De Paul-André Melliès
De Noam Zeilberger
De Vincent Rivasseau
De Joseph Ben Geloun
De Darij Grinberg
De Stéphane Gaubert
De Natalia Iyudu
De Dominique Manchon
De Richard Kerner
De Gérard Ben Arous
De Giulio Biroli
De Giulio Biroli
De Gérard Ben Arous
De Gérard Ben Arous
