Geodesic
On the index of $G$-spaces
Sbornik. Mathematics, Tome 191 (2000) no. 9, pp. 1259-1277

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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. 
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     author = {A. Yu. Volovikov},
     title = {On the index of $G$-spaces},
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     number = {9},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2000_191_9_a0/}
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A. Yu. Volovikov. On the index of $G$-spaces. Sbornik. Mathematics, Tome 191 (2000) no. 9, pp. 1259-1277. http://geodesic.mathdoc.fr/item/SM_2000_191_9_a0/