Postnikov towers and Gottlieb groups of orbit spaces

Marek Golasiński and Daciberg Lima Gonçalves

Vol. 197 (2001), No. 2, 291–300

DOI: 10.2140/pjm.2001.197.291

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.

Milestones

Received: 7 August 1998

Revised: 20 January 2000

Published: 1 February 2001