Geometry and topology · Jul 19, 2026
Jacobian conjecture in dimension three
An explicit map in C^3 with det JF=-2 and three different points having the same image; padding gives higher-dimensional counterexamples.
Scope and what remains
The complex dimension-two question remains open. The displayed coordinate degrees are 7, 6 and 4: the cubic fiber equation is not a cubic coordinate map. Do not transfer a disproof to a related conjecture without its precise reduction.
Contributors
Levent Alpöge with Claude Fable 5, according to the announcement attribution. Shuhong Gao provides a separate algebraic/geometric analysis; later family constructions are distinct contributions.
AI systems: Claude Fable 5