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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Rational Moore $ G$-spaces


Author: Peter J. Kahn
Journal: Trans. Amer. Math. Soc. 298 (1986), 245-271
MSC: Primary 55N25; Secondary 55P62, 55Q05, 57S17
DOI: https://doi.org/10.1090/S0002-9947-1986-0857443-9
MathSciNet review: 857443
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Abstract: This paper obtains some existence and uniqueness results for Moore spaces in the context of the equivariant homotopy theory of Bredon. This theory incorporates fixed-point-set data as part of the structure and so is a refinement of the classical equivariant homotopy theory. To avoid counterexamples to existence in the classical case and to focus on new phenomena involving the fixed-point-set structure, most of the results involve rational spaces. In this setting, there are no obstacles to existence, but a notion of projective dimension presents an obstacle to uniqueness: uniqueness is proved, subject to constraint on the projective dimension, and an example shows that this constraint is sharp. Various related existence results are proved and computations are given of certain equivariant mapping sets $ [X,\,Y]$, $ X$ an equivariant Moore space.


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DOI: https://doi.org/10.1090/S0002-9947-1986-0857443-9
Keywords: Moore space, equivariant, $ G$-space, homotopy
Article copyright: © Copyright 1986 American Mathematical Society