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VIDEO LIBRARY |
Adian 90: Conference on Mathematical Logic, Algebra, and Computation
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On a tropical version of the Jacobian conjecture D. Yu. Grigor'ev Institut des Mathématiques de Lille, France |
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Abstract: 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. Joint work with Danylo Radchenko. Language: English |