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

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

2006-12-14

arxiv.org/abs/math/0612386v1

Mathematics

Geometric Topology

27 pages, 0 figures

Scientific paper

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 $K(\pi_{1}(X),1)$.

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