On the index of a vector field at an isolated singularity

We consider manifolds with isolated singularities, i.e., topological spaces which are manifolds (say, C"#infinity#-) outside discrete subsets (sets of singular points). For (germs of) manifolds with, so called, cone-like singularities, a notion of the index of an isolated singular point of a vector field is introduced. There is given a formula for the index of a gradient vector field on a (real) isolated complete intersection singularity. The formula is in terms of signatures of certain quadratic forms on the corresponding spaces of thimbles. (orig.)Available from TIB Hannover: RN 3109(285) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman