ON THE RELATION BETWEEN INDEX AND MULTIPLICITY.

This paper is mainly devoted to the study of the index of a map at a zero, and the index of a polynomial map over Rn. For semi-quasi-homogeneous maps we prove that the index at a zero coincides with the index at this zero of its quasi-homogeneous part. For a class of polynomial maps with finite zero set we provide a method which makes easier the computation of its index over Rn. Finally we relate the index and the multiplicity. [ABSTRACT FROM AUTHOR]