Unstable 𝑣₁-periodic homotopy groups of a Moore space

Abstract

The mod ⁡ p v 1 \operatorname {mod} p\quad {v _1} -periodic homotopy groups of a space X X are defined by considering the homotopy classes of maps of a Moore space into X X and then inverting the Adams self-map of a Moore space. In this paper the mod ⁡ p v 1 \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 {v _1} -periodic homotopy groups induced by the Adams map is an isomorphism.