Abstract

Let X be a 1-connected space with the homotopy type of a CW-space and H a finite group acting freely on X by homeomorphisms homotopic to the identity. We prove that l_kη_*G_k(X) ⊆ G_k(X ∕ H) for all k > 1 and some estimated positive integer l_k which depends on k, where G_k is the k′th Gottlieb group and η : X → X ∕ H is the quotient map to the orbit space X ∕ H. We show that l_k is independent of k for X with the homotopy type of a finite CW-space. We also obtain that lπ_k(X) ⊆ G_k(X) for some positive integer l (independent on k) provided some restrictions are placed on the space X and the integer k > 1. Moreover, η_*G_k(X)_p = G_k(X ∕ H)_p for the p-primary components, where p is a prime not dividing the order |H| of the group H.

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