%0 Journal Article
%T On the homotopy of finite CW-complexes with polycyclic fundamental group
%A Mihai Damian
%J Mathematics
%D 2006
%I arXiv
%X Let X be a finite CW-complex of dimension q. If its fundamental group $\pi_{1}(X)$ is polycyclic of Hirsch number h>q we show that at least one of the homotopy groups $\pi_{i}(X)$ is not finitely generated. If h=q or h=q-1 the same conclusion holds unless X is an Eilenberg-McLane space $K(\pi_{1}(X),1)$.
%U http://arxiv.org/abs/math/0612386v1