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An ideal-valued cohomological index theory with applications to Borsuk—Ulam and Bourgin—Yang theorems

Published online by Cambridge University Press:  10 December 2009

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Abstract

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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 8 , Volume 8: Charles Conley Memorial Issue , December 1988 , pp. 73 - 85
Copyright
Copyright © Cambridge University Press 1988

References

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