An ideal-valued cohomological index theory with applications to Borsuk—Ulam and Bourgin—Yang theorems
An ideal-valued cohomological index theory with applications to Borsuk—Ulam and Bourgin—Yang theorems
复制标题
理想值上同调指数理论及其在 Borsuk-Ulam 和 Bourgin-Yang 定理中的应用
DOI：
10.1017/s0143385700009342
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发表时间：
1988
影响因子：
0.9
通讯作者：
S. Husseini
中科院分区：
文献类型：
--
作者：
E. Fadell;S. Husseini
B上G-对（X，A）的数值上同调指标理论，其中G是紧李群，在临界点理论和Borsuk-Ulam定理及Bourgin-Yang定理的证明中已被证明是有用的.使用理想值理论获得了更多的信息（在取数值时丢失），并且该理论被应用于估计从某些G-流形到G-模的G-映射的零点集的大小。这些定理的参数化版本也得到了一个原则，适用相当普遍。
Abstract Numerical-valued cohomological index theories for G-pairs (X, A) over B, where G is a compact Lie group, have proved useful in critical point theory and in proving Borsuk—Ulam and Bourgin—Yang theorems. More information (which is lost in taking numerical values) is obtained using an ideal-valued theory, and this theory is applied to estimating the size of the zero set of a G-map from certain G-manifolds to a G-module. Parametrized versions of these theorems are also obtained by a principle which applies quite generally.