Radial index related to an intersection index

Julie Lapebie

Journal of Singularities
volume 17 (2018), 403-412

Received: 20 March 2018. Received in revised form: 13 November 2018.

DOI: 10.5427/jsing.2018.17r

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Abstract:

On a closed semialgebraic set X with an isolated singularity at 0, we consider a vector field V with an isolated singularity at 0 and study its radial index at the singularity. We first prove a relation between this index and the radial index at 0 of the vector field -V and give some corollaries of this formula. Then we express the radial index of V at 0 in terms of the intersection index of two submanifolds of a certain bundle defined over the link of the singularity.


Keywords:

Radial index, semialgebraic set, Euler characteristic


Mathematical Subject Classification (2010):

14P10, 14P25, 58K05


Author(s) information:

Julie Lapebie
Aix-Marseille Université
CNRS, Centre Gilles-Gaton Granger
Aix-en-Provence, France
email: julie.lapebie@univ-amu.fr