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

Abstract

AbstractThe 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 singular semi-analytic sets innthat 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 fields defined onn.