On the 3-Type of a Complex

Abstract

1. Introduction.-The standard algebraic invariants of a topological space depend only on the homotopy type of the space. This note will deal with part of the converse problem of the determination of the homotopy type by algebraic invariants, and will show in effect that the only one-and two-dimensional invariants which enter are the fundamental group 7rl, the second homotopy group 7r2, and a certain three-dimensional co-homology class of 7r, in 7r2.