On the index of G-spaces
On the index of G-spaces
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关于 G 空间的索引
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
A. Volovikov
中科院分区：
文献类型：
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作者：
A. Volovikov
对于G-空间，其中G是紧李群，人们可以在G的分类空间的上同调环中关联一个理想。它被称为G-空间的理想值指数。被认为是一个过滤的理想值的指数，产生在一个自然的方式从勒雷谱序列。研究了滤色指数的性质，并引入了数值指数。这类指标便于G-范畴的估计和流形上G-不变泛函临界点集的研究，并证明了带滤子指标的Bourgin-Yang定理的推广.这一结果被用于估计的指数的空间的部分重合的映射的空间与p-环面行动的欧几里德空间。
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.