FIBER SQUARES AND COMPLEXES

In this paper we wish to examine the classification of finite two-dime nsional CW-complexes with finite fundamental group by decomposing the cellular chain complex of the universal cover via a fiber square of ri ngs. The bias invariant of Dyer and Sieradski is shown to arise in thi s context as one of three obstructions to homotopy equivalence and som e quite natural questions are posed.