Free torus actions and twisted suspensions
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 acti...
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Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Sigma |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509424001415/type/journal_article |
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| author | Fernando Galaz-García Philipp Reiser |
| author_facet | Fernando Galaz-García Philipp Reiser |
| author_sort | Fernando Galaz-García |
| collection | DOAJ |
| description | 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 | Article |
| id | doaj-art-5f1fc85ed4974178b7d7e3663b015e07 |
| institution | Kabale University |
| issn | 2050-5094 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj-art-5f1fc85ed4974178b7d7e3663b015e072025-01-20T06:07:59ZengCambridge University PressForum of Mathematics, Sigma2050-50942025-01-011310.1017/fms.2024.141Free torus actions and twisted suspensionsFernando Galaz-García0https://orcid.org/0000-0003-3428-5190Philipp Reiser1https://orcid.org/0000-0002-7997-7484Department of Mathematical Sciences, Durham University, Upper Mountjoy Campus, Stockton Rd, Durham DH1 3LE, United Kingdom; E-mail: .Department of Mathematics, University of Fribourg, Chem. du Musée 23, 1700 Fribourg, SwitzerlandWe 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.https://www.cambridge.org/core/product/identifier/S2050509424001415/type/journal_article57S1555R1553C2057R6557R2255R25 |
| spellingShingle | Fernando Galaz-García Philipp Reiser Free torus actions and twisted suspensions Forum of Mathematics, Sigma 57S15 55R15 53C20 57R65 57R22 55R25 |
| title | Free torus actions and twisted suspensions |
| title_full | Free torus actions and twisted suspensions |
| title_fullStr | Free torus actions and twisted suspensions |
| title_full_unstemmed | Free torus actions and twisted suspensions |
| title_short | Free torus actions and twisted suspensions |
| title_sort | free torus actions and twisted suspensions |
| topic | 57S15 55R15 53C20 57R65 57R22 55R25 |
| url | https://www.cambridge.org/core/product/identifier/S2050509424001415/type/journal_article |
| work_keys_str_mv | AT fernandogalazgarcia freetorusactionsandtwistedsuspensions AT philippreiser freetorusactionsandtwistedsuspensions |