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. Pr...

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Bibliographic Details
Published in:Sbornik. Mathematics 2000-10, Vol.191 (9)
Main Author: Volovikov, A Yu
Format: Article
Language:English
Subjects:
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
EUCLIDEAN SPACE
LIE GROUPS
YANG THEOREM
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Summary: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.
ISSN:1064-5616
1468-4802
DOI:10.1070/SM2000V191N09ABEH000504;COUNTRYOFINPUT:INTERNATIONALATOMICENERGYAGENCY(IAEA)