Polynomial atlases on manifolds
Nicholas Juricic

TL;DR
This paper explores manifolds with polynomial transition maps to provide an equivalent formulation of the Jacobian conjecture over the real numbers, connecting geometric structures with a major open problem in algebraic geometry.
Contribution
It introduces polynomial atlases on manifolds as a new framework to restate the Jacobian conjecture, bridging differential geometry and algebraic geometry.
Findings
Equivalent formulation of the Jacobian conjecture using polynomial atlases
Establishment of a geometric perspective on a longstanding algebraic problem
Potential new approaches to solving the Jacobian conjecture
Abstract
We consider manifolds whose transition maps are restrictions of polynomial mappings , and use them to give an equivalent statement of the Jacobian conjecture over the real field.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Control and Dynamics of Mobile Robots · Advanced Differential Geometry Research
