The contact boundary of a complex polynomial |
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| Authors: | Clément Caubel Mihai Tibăr |
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| Institution: | (1) Département de Mathématiques, Université de Cergy-Pontoise, 95033 Cergy-Pontoise, France. e-mail: caubel@math.u-cergy.fr, FR;(2) Mathématiques, UMR-CNRS 8524, Université de Lille 1, 59655 Villeneuve d'Ascq, France. e-mail: tibar@agat.univ-lille1.fr, FR |
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| Abstract: | We define the contact boundary of a complex polynomial f : ℂ
n
→ ℂ as the intersection of some generic fiber with a large sphere. We show that, up to contact isotopy, this does not depend
on the choice of the fiber (provided it is generic) and is invariant under polynomial automorphism of ℂ
n
. We next prove that the formal homotopy class of this contact boundary is invariant in a large family of deformations of
polynomials, which are not necessarily topologically trivial.
Received: 15 November 2002
Published online: 20 March 2003
Mathematics Subject Classification (2000): 32S55, 53D15, 32S50 |
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| Keywords: | |
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