Unstable -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 -periodic homotopy groups of a space are defined by considering the homotopy classes of maps of a Moore space into and then inverting the Adams self-map of a Moore space. In this paper the -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 -periodic homotopy groups induced by the Adams map is an isomorphism.

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DOI:
https://doi.org/10.1090/S0002-9939-1989-0976364-2

Article copyright:
© Copyright 1989
American Mathematical Society