Polynomial maps R²→R² with one component of degree 6 and nowhere-zero Jacobian are injective.
Oka , Note on estimation of the number of the critical values at infinity , in: W orkshop on Geometry and Topology, Hanoi, 1993, in: Kod ai Math
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The real Jacobian conjecture for maps with one component having degree 6
Polynomial maps R²→R² with one component of degree 6 and nowhere-zero Jacobian are injective.