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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Unstable $ v\sb 1$-periodic homotopy groups of a Moore space


Author: Robert D. Thompson
Journal: Proc. Amer. Math. Soc. 107 (1989), 833-845
MSC: Primary 55Q52; Secondary 55T15
MathSciNet review: 976364
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Abstract: The $ \operatorname{mod} p\quad {v _1}$-periodic homotopy groups of a space $ X$ are defined by considering the homotopy classes of maps of a Moore space into $ X$ and then inverting the Adams self-map of a Moore space. In this paper the $ \operatorname{mod} p\quad {v _1}$-periodic homotopy groups of a Moore space are computed by using the Cohen-Moore-Neisendorfer splitting of the space of loops on a Moore space. The Adams map is shown to be compatible with this splitting and it is proved that the homomorphism of $ {v _1}$-periodic homotopy groups induced by the Adams map is an isomorphism.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0976364-2
PII: S 0002-9939(1989)0976364-2
Article copyright: © Copyright 1989 American Mathematical Society