A reformulated version of the Maximal Symmetry Rank conjecture for non-negative curvature states: Maximal Symmetry Rank Conjecture. Let T^k act isometrically and effectively on M^n, a closed, simply-connected, non-negatively curved Riemannian manifold. Then: 1) k r) S^(2n_i) with r\ge 2k-n; or if n\neq 0 mod 3, the quotient of N by the free linear action of a torus of rank