Notes on proper homotopy theories associated with compact PL-manifolds

The purpose of this note is to present a bigraded sequence of functors associated with compact PL-manifolds . These functors are invariant of proper homotopy type, and distinguish topological spaces which have the same homotopy type. On the category of compact topological spaces these functors agree with the Hurewicz homotopy groups, hence the principal interest of these functors is for noncompact spaces