On the Mislin genus of certain circle bundles and noncancellation

Abstract

In an earlier paper, the authors proved that a process described much earlier for passing from a finitely generated nilpotent groupNof a certain kind to a nilpotent spaceXof finite type produced a bijection of Mislin genera𝒢(N)≅𝒢(X). The present paper is concerned with related results obtained by weakening the restrictions onNand generalizing the homotopical nature of the spacesXto be associated with a givenN.