Algebraic Topology of Certain Sasaki Joins
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911845966675968 |
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| author | Castaneda, Candelario Staffeldt, Ross |
| author_facet | Castaneda, Candelario Staffeldt, Ross |
| contents | The join construction produces a third Sasaki manifold from two others, and we investigate the algebraic topology of the joins of circle bundles over surfaces of positive genus with weighted three-spheres. Topologically, such a join has the structure of a lens space bundle over a surface. We calculate invariants determined by the fundamental group, the homology, and the cohomology. We find that, in general, there is torsion in the integral homology of the join. The torsion gives rise to two linking forms, and we identify these linking forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13005 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Algebraic Topology of Certain Sasaki Joins Castaneda, Candelario Staffeldt, Ross Algebraic Topology Primary: 53C25, Secondary: 57R15, 57R15 The join construction produces a third Sasaki manifold from two others, and we investigate the algebraic topology of the joins of circle bundles over surfaces of positive genus with weighted three-spheres. Topologically, such a join has the structure of a lens space bundle over a surface. We calculate invariants determined by the fundamental group, the homology, and the cohomology. We find that, in general, there is torsion in the integral homology of the join. The torsion gives rise to two linking forms, and we identify these linking forms. |
| title | Algebraic Topology of Certain Sasaki Joins |
| topic | Algebraic Topology Primary: 53C25, Secondary: 57R15, 57R15 |
| url | https://arxiv.org/abs/2404.13005 |