Unstable 𝑣₁-periodic homotopy groups of a Moore space

Thompson, Robert D.

doi:10.1090/S0002-9939-1989-0976364-2

Unstable $v_ 1$-periodic homotopy groups of a Moore space
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Proc. Amer. Math. Soc. 107 (1989), 833-845 Request permission

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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A commentary on ’The image of

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