Milnor conjectured that any open n-manifold of non-negative Ricci curvature has a finitely generated fundamental group. In this talk, we use equivariant Gromov-Hausdorff convergence and Cheeger-Colding theory to approach this conjecture in low dimensions. We present a proof in dimension 3; in dimension 4, we confirm Milnor conjecture when the universal cover has Euclidean volume growth and unique tangent cone at infinity.

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