International Journal of Mathematics and Mathematical Sciences 
Volume 24 (2000), Issue 8, Pages 539-548
doi:10.1155/S0161171200002854

On the Mislin genus of certain circle bundles and noncancellation

Peter Hilton1,2 and Dirk Scevenels3

 1Department of Mathematical Sciences, SUNY, Binghamton 13902-6000, NY, USA
2Department of Mathematics, University of Central Florida, Orlando 32816-1364, FL, USA
3Departement Wiskunde, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, Heverlee B-3001, Belgium
Received 1 February 1999

Abstract

In an earlier paper, 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 𝒢(N)≅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.