trailNo known construction converts the three-dimensional Jacobian counterexamples into a counterexample over the complex plane
Every polynomial map of ℂ² with nonzero constant Jacobian determinant has a polynomial inverse
Proved obstruction to graded descent· for
Every polynomial Keller map of the complex plane that is equivariant for a nontrivial multiplicative-group action is a polynomial automorphism
atomic
Vitushkin's construction method faces an obstruction in two dimensions that the three-dimensional polynomial counterexample circumvents
Vitushkin's 1999 paper constructs a non-injective rational self-map of C² with constant nonzero Jacobian
The 2026 Jacobian conjecture counterexample closely parallels Vitushkin's 1999 rational construction lifted to three dimensions
✓
The 2026 three-dimensional Jacobian conjecture counterexample is homogeneous for a mixed-sign integer grading of its coordinates
The plane is uniformly reported untouched· for
A counterexample to the Jacobian conjecture in dimension n yields a counterexample in every dimension m ≥ n by adjoining identity coordinates
atomic
The two-dimensional Jacobian conjecture remains open
atomic
assumed
The Jacobian conjecture is false in every dimension n ≥ 3
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No known construction converts the three-dimensional Jacobian counterexamples into a counterexample over the complex plane
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1depended on by
this rests on ↓
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