Classification of the congruence classes of $$A_n^5$$ (n ⩾ 6) with 2-torsion free homology

Abstract

In this paper, we classify the congruence classes of ${\boldsymbol~F}^5_{n(2)}$-polyhedra, i.e., $(n-1)$-connected, at most $(n+5)$-dimensional polyhedra with 2-torsion free homology. The proof relies on the matrix problem technique which was developed in the classification of representations of algebras and applied to the homotopy theory by Baues and Drozd (1999).