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We classify closed, simply connected n-manifolds of non-negative sectional curvature admitting an isometric torus action of maximal symmetry rank in dimensions 2 ≤ n ≤ 6. In dimensions 3k, k = 1, 2 there is only one such manifold and it is diffeomorphic to the product of k copies of the 3-sphere.doi:10.1090/s0002-9939-2010-10655-x fatcat:o4otp5hbdfczrmojwqbymbnzee