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On the classification of full factors of type III

We introduce a new invariant S(M) for type III factors M with no almost-periodic weights. We compute this invariant for certain free Araki-Woods factors. We show that Connes' invariant r cannot distinguish all isomorphism classes of free Araki-Woods factors. We show that there exists a continuum of mutually non-isomorphic free Araki-Woods factors, each without almost-periodic weights.