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Transactions of the American Mathematical Society

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



Stable maps into free $ G$-spaces

Author: J. P. C. Greenlees
Journal: Trans. Amer. Math. Soc. 310 (1988), 199-215
MSC: Primary 55P42; Secondary 55T15
MathSciNet review: 938918
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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 $ \S1$. 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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Keywords: Adams spectral sequence, Borel cohomology, equivariant cohomology, Segal conjecture, Singer construction
Article copyright: © Copyright 1988 American Mathematical Society