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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 liave the same homotopy type . On the category of compact topological spaces thesifunctors agree with the llurewicz homotopy groups, hence the principal interest of these functors is for noncompact spaces . Consider the category of compact PL-manifolds and the bordism theory between thesedoi:10.5565/publmat_26382_02 fatcat:r56djup7rfej3j5t436nvdm5zu