A n 4 -polyhedra with free homology

Abstract

An A n k -polyhedron is a CW-complex which is (n−1)-connected and of dimension ≤(n+k). We compute an algebraic category which is equivalent to the homotopy category of A n 2 -polyhedra with free homology (n≥3). This computation and a calculation of the Γ-group Γn+3(X) (n≥3) is used to obtain a complete algebraic homotopy invariant for A n 4 -polyhedra with free homology (n≥3). As an application we compute the group of self-homotopy equivalences Aut(X) for a bouquet X=∨∑ℂP2.