Comptes Rendus
no. 12
Non-reality and non-connectivity of complex polynomials
[Non réalité et non connectivité des polynômes complexes]
Arnaud Bodin1
1 Laboratoire Agat, UFR de mathématiques, Université Lille 1, 59655 Villeneuve d'Ascq cedex, France
Comptes Rendus. Mathématique, Volume 335 (2002) no. 12, pp. 1039-1042.

Pour les polynômes de deux variables complexes, nous construisons des contre-exemples aux questions suivantes : à équivalence topologique près, peut-on toujours trouver une équation réelle à un polynôme complexe (Lee Rudolph) ? Deux polynômes topologiquement équivalents peuvent-ils être reliés par une famille de polynômes topologiquement équivalents ?

Using the same method we provide negative answers to the following questions: is it possible to find real equations for complex polynomials in two variables up to topological equivalence (Lee Rudolph)? Can two topologically equivalent polynomials be connected by a continuous family of topologically equivalent polynomials?

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02597-9
Arnaud Bodin 1

1 Laboratoire Agat, UFR de mathématiques, Université Lille 1, 59655 Villeneuve d'Ascq cedex, France 
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Arnaud Bodin. Non-reality and non-connectivity of complex polynomials. Comptes Rendus. Mathématique, Volume 335 (2002) no. 12, pp. 1039-1042. doi : 10.1016/S1631-073X(02)02597-9. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02597-9/

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