Actions on 2-complexes and the homotopical invariant Sigma(2) of a group

[摘要] 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 -->--> X. From this we deduce two criteria for the computation of the homotopical invariant Sigma(?)2(G) introduced by B. Rent (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 Sigma(m)-conjecture for metabelian groups of finite Prufer rank. (C) 1997 Elsevier Science B.V.

[发布日期] 1997-07-07