Free torus actions and twisted suspensions
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866913667194290176 |
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| author | Galaz-García, Fernando Reiser, Philipp |
| author_facet | Galaz-García, Fernando Reiser, Philipp |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_06068 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Free torus actions and twisted suspensions Galaz-García, Fernando Reiser, Philipp Geometric Topology Differential Geometry 57S15 (Primary) 55R15, 53C20, 57R65, 57R22, 55R25 (Secondary) 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. |
| title | Free torus actions and twisted suspensions |
| topic | Geometric Topology Differential Geometry 57S15 (Primary) 55R15, 53C20, 57R65, 57R22, 55R25 (Secondary) |
| url | https://arxiv.org/abs/2305.06068 |