The homotopy classification of \((n-1)\)-connected \((n+4)\)-dimensional polyhedra with torsion free homology, \(n\geq 5\) (Q1293765)

The authors study the classification problem of the homotopy types of \((n-1)\)-connected \((n+k)\)-dimensional polyhedra \(X\) with torsion free homology. When \(n\geq k+1\), it follows from the Freudenthal suspension theorem that this classification problem depends only on \(k\) and not on \(n\) and they study this problem in this situation. Since the classification is solved for \(k\leq 3\), they consider the case \(k=4\) in this paper. They obtain the complete classification of homotopy types for the case \(k=4\). In particular, they give the complete list \(X(\mathcal L)\) consisting of exactly 67 polyhedra such that, if \(X\) is an \((n-1)\)-connected \((n+4)\)-dimensional polyhedron \(X\) with torsion free homology \((n\geq 5)\), then there is a homotopy equivalence \(X\simeq \bigvee_{j=1}^k X_j\) with each \(X_j\in X(\mathcal L)\).