Radial index and Poincar\'e-Hopf index of 1-forms on semi-analytic sets

The radial index of a 1-form on a singular set is a generalization of the classical Poincar\'e-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 Poincar\'e-Hopf indices at 0 of vector fiels defined on R^n.