Algebraic properties of decorated splitting obstruction groups

A. Cavicchioli; Y. V. Muranov; D. Repovš

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In this paper, we generalize the equivariant homotopy groups or equivalently the Rhodes groups. We establish a short exact sequence relating the generalized Rhodes groups and the generalized Fox homotopy groups and we introduce Γ-Rhodes groups, where Γ admits a certain co-grouplike structure. Evaluation subgroups of Γ-Rhodes groups are discussed.