Homotopy invariants of nonsimply connected manifolds. I. Rational invariants

Invariants of nonsimply connected manifolds are investigated of the same type as the signature of a manifold, or of “higher signature” for manifolds with free Abelian fundamental group, which correspond to the possibility of surgery on a manifold. It is proved that these invariants depend only on the homotopy type of the manifold and a bordism class of manifolds.