Higher homotopy invariants for spaces and maps

For a pointed topological space X, we use an inductive construction of a simplicial resolution of X by wedges of spheres to construct a “higher homotopy structure” for X (in terms of chain complexes of spaces). This structure is then used to define a collection of higher homotopy invariants which suffice to recover X up to weak equivalence. It can also be used to distinguish between different maps f: X →Y which induce the same morphism f_*: π_*X → π_*Y.