Polynomial maps R²→R² with one component of degree 6 and nowhere-zero Jacobian are injective.
Koll ´ar, Lectures on resolution of singularities , Princeton University Press, 2009, vi+208 pp
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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.