## 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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*Prerequisites*(

*on equivariant stable homotopy*)

*for Carlssonβs lecture*, Lecture Notes in Math., vol. 1051, Springer-Verlag, 1984, pp. 483-532.

*Borel homology*I, Preprint (1987). β,

*Borel homology*II (in preparation). β,

*Homotopy equivariance strict equivariance and the Segal conjecture*(in preparation).

*Equivariant cohomology theory*(in preparation).

*Equivariant*$RO(G)$-

*graded singular cohomology*, Preprint (1979).

## Bibliographic Information

- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**310**(1988), 199-215 - MSC: Primary 55P42; Secondary 55T15
- DOI: https://doi.org/10.1090/S0002-9947-1988-0938918-2
- MathSciNet review: 938918