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

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

2007-02-21

arxiv.org/abs/math/0702607v2

Journal of Pure and Applied Algebra, Vol 212 (2008), 1664-1673.

Mathematics

Algebraic Topology

16 pages; some little corrections and improvements have been made. To appear in J. Pure and Applied Algebra

Scientific paper

10.1016/j.jpaa.2007.11.002.

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 question we address here is to characterize 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.

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