Narrow Results

Let M be a closed even n-manifold of positive sectional curvature on which a torus T^k acts isometrically. We show that if (respectively, k > 1) for n ≠ 12 (respectively, n = 12), then the Euler characteristic of each T^k-fixed point component is positive. This implies that the Euler characteristic of M is positive. We also extend this result to an isometric elementary p-group -action on a closed manifold of positive sectional curvature.

In this paper, we obtain a classification for the fundamental groups of positively curved n-manifolds which admit isometric torus T^k-actions with and n ≥ 25.