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Counterexamples to the Jacobian conjecture in dimensions greater than two
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On July 19, 2026, the conjecture was refuted in dimension three by an explicit counterexample announced by L. Alpöge.
Alpöge's map (a,b,c) on ℂ³ has constant Jacobian determinant −2 yet is generically three-to-one
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- Sep 14, 2026Entered the graphEntered the graph; copy stored