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Transactions of the American Mathematical Society

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On an extension of localization theorem and generalized Conner conjecture

Authors: Satya Deo, Tej Bahadur Singh and Ram Anugrah Shukla
Journal: Trans. Amer. Math. Soc. 269 (1982), 395-402
MSC: Primary 57S10
MathSciNet review: 637697
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Abstract: Let $ G$ be a compact Lie group. Then Borel-Segal-Quillen-Hsiang localization theorems are known for any $ G$-space $ X$ where $ X$ is any compact Hausdorff space or a paracompact Hausdorff space of finite cohomology dimension. The Conner conjecture proved by Oliver and its various generalizations by Skjelbred are also known for only these two classes of spaces. In this paper we extend all of these results for the equivariant category of all finitistic $ G$-spaces. For the case when $ G = {Z_p}$ or $ G = T$ (torus) some of these results were already proved by Bredon.

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Article copyright: © Copyright 1982 American Mathematical Society