A new topological proof of the Abhyankar-Moh theorem
The paper presents a new proof of the known Abhyankar-Moh theorem on embeddings of the line in the plane [\textit{S. Abhyankar} and \textit{T. Moh}, J. Reine Angew. Math. 276, 148--166 (1975; Zbl 0332.14004)] that for any injective polynomial mapping \(\Phi :\mathbb C\to \mathbb C^2\) without critical points the image of \(\Phi \) can be transformed to a straight line by a polynomial automorphism of \(\mathbb C^2\). The proof relies on the Poincaré-Hopf theorem on the Euler characteristic of a compact real manifold.
scientific article; zbMATH DE number 1983492