Published online by Cambridge University Press: 26 February 2010
Kan and Thurston, in their paper [5], asked whether each smooth closed manifold other than S2 or RP2 has the same integral homology as a closed aspherical manifold. F. E. A. Johnson in [3], [4] is concerned with the answer to this question when the smooth closed manifold is an n-dimensional sphere Sn. He asked whether there exist aspherical manifolds Xг which have the homology of Sn.