Radial index and Poincaré-Hopf index of 1-forms on semi-analytic sets

Nicolas Dutertre (1)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

The radial index of a 1-form on a singular set is a generalization of the classical Poincaré-Hopf index. We consider different classes of closed semi-analytic sets in R^n that contain 0 in their singular locus and we relate the radial index of a 1-form at 0 on these sets to Poincaré-Hopf indices at 0 of vector fiels defined on R^n.

Mots clés: singular varieties; 1-forms; indices

Domaines: Géométrie algébrique [math.AG]

Nicolas Dutertre. Radial index and Poincaré-Hopf index of 1-forms on semi-analytic sets. Mathematical Proceedings of the Cambridge Philosophical Society, 2010, 148 (2), pp.297-330. ⟨hal-00367729⟩