ACTIONS ON 2-COMPLEXES AND THE HOMOTOPICAL INVARIANT SIGMA(2) OF A GROUP

Given a group G acting on a 2-complex X we construct, depending on sev eral choices, a 2-complex Y with free G-action together with a G-equiv ariant map p:Y -->--> X. From this we deduce two criteria for the comp utation of the homotopical invariant Sigma(?)2(G) introduced by B. Ren t (Geometric invariants and HNN-extensions, in: K.N. Cheng and Y.K. Le ong, Eds., Group Theory (de Gruyter, Berlin, 1989) 465-484). These res ults are used to complete the proof of the Sigma(m)-conjecture for met abelian groups of finite Prufer rank. (C) 1997 Elsevier Science B.V.