I will give a survey lecture on the classification of outer actions of amenable groups on von Neumann algebras with the main focus being on II_1 factors. I will introduce the fundamental uniqueness theorem of Ocneanu and his results on vanishing of 2-cohomology. Next, I present more recent work of Sorin Popa on this vanishing of 2-cohomology for actions of amenable groups on arbitrary II_1 factors.
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