Topology of Complex Polynomials and Jacobian Conjecture

The purpose of this paper is to report on some new results on the Topology of Complex Polynomials f :C2→C. These results lead to an open problem closely related to the Jacobian Conjecture. Works by S.A. Broughton [Invent. Math. 92 (1988) 217], A. Dimca [Singularities and Topology of Hypersurfaces, Springer, 1992] and LeDung Trang, C. Weber [C. R. Acad. Sci. Paris 320 (1995) 581] can provide more insight into the problem and J. Milnor [Singular Points of Complex Hypersurfaces, Princeton Univ. Press, 1988] is a good reference for general information on the subject. The main result proved here is similar to one proved by R. Ephraim [Proc. Sympos. Pure Math., Vol. 40, 1983, p. 353, Corollary 3.14], but our proof is short and clearer due to the use of Ha–Lê Theorem. Also, we bring new light to the points at infinity.