Sphere bundles over $4$-manifolds are trivial after looping
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910920982134784 |
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| author | Huang, Ruizhi |
| author_facet | Huang, Ruizhi |
| contents | We show that except two special cases, the sphere bundle of a vector bundle over a simply connected $4$-manifold splits after looping. In particular, this implies that though there are infinitely many inequivalent sphere bundles of a given rank over a $4$-manifold, the loop spaces of their total manifolds are all homotopy equivalent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_17352 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Sphere bundles over $4$-manifolds are trivial after looping Huang, Ruizhi Algebraic Topology Geometric Topology We show that except two special cases, the sphere bundle of a vector bundle over a simply connected $4$-manifold splits after looping. In particular, this implies that though there are infinitely many inequivalent sphere bundles of a given rank over a $4$-manifold, the loop spaces of their total manifolds are all homotopy equivalent. |
| title | Sphere bundles over $4$-manifolds are trivial after looping |
| topic | Algebraic Topology Geometric Topology |
| url | https://arxiv.org/abs/2210.17352 |