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ON TOPOLOGICAL INVARIANTS ASSOCIATED WITH A POLYNOMIAL WITH ISOLATED CRITICAL POINTS

Published online by Cambridge University Press:  19 May 2004

NICOLAS DUTERTRE
NICOLAS DUTERTRE
Affiliation:
Université de Provence, Centre de Mathématiques et Informatique, 39 rue Joliot-Curie, 13453 Marseille Cedex 13, France e-mail: dutertre@cmi.univ-mrs.fr
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Abstract

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We consider a polynomial $f \,{:}\, \mathbb{R}^n \rightarrow \mathbb{R}$ with isolated critical points and we relate $\chi(f^{-1}(0))$ and $\chi(\{f \ge 0\})-\chi(\{f \le 0\})$ to the topological degrees of polynomial maps defined in terms of $f$.

Keywords

14P25
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 46 , Issue 2 , May 2004 , pp. 323 - 334
Copyright
2004 Glasgow Mathematical Journal Trust