Rational Moore 𝐺-spaces

Kahn, Peter J.

doi:10.1090/S0002-9947-1986-0857443-9

Rational Moore $G$-spaces
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by Peter J. Kahn

Trans. Amer. Math. Soc. 298 (1986), 245-271

DOI: https://doi.org/10.1090/S0002-9947-1986-0857443-9

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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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