Computability of homotopy groups of nilpotent complexes (Q1092451)

In 1956 E. H. Brown proved the following theorem. Let X be a 1-connected locally finite, simplicial complex. Then \(\Pi_ n(X)\) is effectively computable. In the present paper, the author generalizes this theorem to the case where X is a nilpotent complex. More precisely, for a nilpotent complex the Postnikov tower does not directly yield a presentation of \(\Pi_ n(X)\). But passing to the (n-1) connected cover of X, there exists a recursive complex, say \(T_ n\), such that \(H_{n+1}(T_ n)\cong \Pi_{n+1}(X)\) is recursively computable.