On the Mislin genus of certain circle bundles and noncancellation (Q5926158)

Summary: In an earlier paper [Proc. Am. Math. Soc. 127, No. 11, 3433-3438 (1999; Zbl 0938.55019)], the authors proved that a process described much earlier for passing from a finitely generated nilpotent group \(N\) of a certain kind to a nilpotent space \(X\) of finite type produced a bijection of Mislin genera \({\mathcal G}(N)\cong {\mathcal G}(X)\). The present paper is concerned with related results obtained by weakening the restrictions on \(N\) and generalizing the homotopical nature of the spaces \(X\) to be associated with a given \(N\).