Free torus actions and twisted suspensions

Galaz Garcia, Fernando; Reiser, Philipp

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.

Citation

Galaz Garcia, F., & Reiser, P. (2025). Free torus actions and twisted suspensions. Forum of Mathematics, Sigma, 13, Article e3. https://doi.org/10.1017/fms.2024.141

• Journal Article Type: Article
• Acceptance Date: Nov 1, 2024
• Online Publication Date: Jan 20, 2025
• Publication Date: 2025-01
• Deposit Date: Dec 14, 2024
• Publicly Available Date: Feb 3, 2025
• Journal: Forum of Mathematics, Sigma
• Print ISSN: 2050-5094
• Electronic ISSN: 2050-5094
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 13
• Article Number: e3
• DOI: https://doi.org/10.1017/fms.2024.141
• Public URL: https://durham-repository.worktribe.com/output/3221522