Actions on 2-complexes and the homotopical invariant Σ2 of a group Original Research Article

Given a group G acting on a 2-complex X we construct, depending on several choices, a 2-complex Y with free G-action together with a G-equivariant map p : Y at X. From this we deduce two criteria for the computation of the homotopical invariant Σ2(G) introduced by B. Renz (Geometric invariants and HNN-extensions, in: K.N. Cheng and Y.K. Leong, Eds., Group Theory (de Gruyter, Berlin, 1989) 465–484). These results are used to complete the proof of the Σm-conjecture for metabelian groups of finite Prüfer rank.