On the index of G-spaces

With a G-space, where G is a compact Lie group, one can associate an ideal in the cohomology ring of the classifying space for G. It is called the ideal-valued index of the G-space. A filtration of the ideal-valued index that arises in a natural way from the Leray spectral sequence is considered. Properties of the index with filtration are studied and numerical indices are introduced. These indices are convenient for estimates of the G-category and the study of the set of critical points of a G-invariant functional defined on a manifold. A generalization of the Bourgin-Yang theorem for the index with filtration is proved. This result is used for estimates of the index of the space of partial coincidences for a map of a space with p-torus action in a Euclidean space