Free torus actions and twisted suspensions

Abstract

We express the total space of a principal circle bundle over a connected sum of two manifolds in terms of the total spaces of circle bundles over each summand, provided certain conditions hold. We then apply this result to provide sufficient conditions for the existence of free circle and torus actions on connected sums of products of spheres and obtain a topological classification of closed, simply-connected manifolds with a free cohomogeneity-four torus action. As a corollary, we obtain infinitely-many manifolds with Riemannian metrics of positive Ricci curvature and isometric torus actions.

Minor changes, final version, to appear in Forum of Mathematics, Sigma

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• Nonconnected Moduli Spaces of Nonnegative Sectional Curvature Metrics on Simply Connected Manifolds
• Ricci-Positive Metrics on Connected Sums of Projective Spaces
• Generalized Surgery on Riemannian Manifolds of Positive Ricci Curvature
• Regular Circle Actions on 2-connected 7-manifolds
• Circle actions and Suspension operations on Smooth manifolds
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Cited by in corpus (3)

• Ricci curvature and minimal hypersurfaces with large Betti numbers
• Free circle actions on certain simply connected $7-$manifolds
• Free circle actions on $(n-1)$-connected $(2n+1)$-manifolds