Topology of Complex Polynomials and Jacobian Conjecture

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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.


This article was originally published in Topology and its Applications. The full-text article from the publisher can be found here.

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Topology and its Applications


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