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On the homotopy of finite CW-complexes with polycyclic fundamental group

Mihai Damian
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Abstract

Let X be a finite CW-complex of dimension q. If its fundamental group $π_{1}(X)$ is polycyclic of Hirsch number h>q we show that at least one of the homotopy groups $π_{i}(X)$ is not finitely generated. If h=q or h=q-1 the same conclusion holds unless X is an Eilenberg-McLane space $K(π_{1}(X),1)$.

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Mihai Damian. 2006-12-14. On the homotopy of finite CW-complexes with polycyclic fundamental group. https://arxiv.org/abs/math/0612386

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