A connection between cellularization for groups and spaces via two-complexes

Abstract Let M denote a two-dimensional Moore space (so H 2 ( M ; Z ) = 0 ), with fundamental group G . The M -cellular spaces are those one can build from M by using wedges, push-outs, and telescopes (and hence all pointed homotopy colimits). The issue we address here is the characterization of the class of M -cellular spaces by means of algebraic properties derived from the group G . We show that the cellular type of the fundamental group and homological information does not suffice, and one is forced to study a certain universal extension.