Abstract:
With a GG-space, where GG is a compact Lie group, one can associate an ideal in the cohomology ring of the classifying space for GG. It is called the ideal-valued index of the GG-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 GG-category and the study of the set of critical points of a GG-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 pp-torus action in a Euclidean space.
\Bibitem{Vol00}
\by A.~Yu.~Volovikov
\paper On the index of $G$-spaces
\jour Sb. Math.
\yr 2000
\vol 191
\issue 9
\pages 1259--1277
\mathnet{http://mi.mathnet.ru/eng/sm504}
\crossref{https://doi.org/10.1070/sm2000v191n09ABEH000504}
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