Stable maps into free 𝐺-spaces

Greenlees, J. P. C.

doi:10.1090/S0002-9947-1988-0938918-2

Stable maps into free $G$-spaces
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by J. P. C. Greenlees

Trans. Amer. Math. Soc. 310 (1988), 199-215

DOI: https://doi.org/10.1090/S0002-9947-1988-0938918-2

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Abstract:

In this paper we introduce a systematic method for calculating the group of stable equivariant maps ${[X, Y]^G}$ [3, 18] into a $G$-free space or spectrum $Y$. In fact the method applies without restriction on $X$ whenever $G$ is a $p$-group and $Y$ is $p$-complete and satisfies standard finiteness assumptions. The method is an Adams spectral sequence based on a new equivariant cohomology theory ${c^{\ast }}(X)$ which we introduce in $\S 1$. This spectral sequence is quite calculable and provides a natural generalisation of the classical Adams spectral sequence based on ordinary $\bmod p$ cohomology. It also geometrically realises certain inverse limits of nonequivariant Adams spectral sequences which have been useful in the study of the Segal conjecture [19, 5, 21, 9].

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