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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.08545 |
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| _version_ | 1866916203301175296 |
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| author | Wang, Yi Yang, Jingye |
| author_facet | Wang, Yi Yang, Jingye |
| contents | For most aspherical Seifert-fibered 3-manifolds $M$, the space of Seifert fiberings $SF(M)$ is known to have contractible components. It is also known that the space of Hopf fiberings of the three-sphere is noncontractible. We provide the second example of a non-aspherical 3-manifold $M$ such that $SF(M)$ has noncontractible components. In particular, we show that certain components of $SF(S^1 \times S^2)$ are homotopy equivalent to a subspace homeomorphic to the identity-based loop space $ΩSO(3)$, and we exhibit second homology generators for both connected components of $SF(S^1 \times S^2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08545 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the homotopy type of the space of fiberings of $S^1 \times S^2$ by simple closed curves Wang, Yi Yang, Jingye Geometric Topology For most aspherical Seifert-fibered 3-manifolds $M$, the space of Seifert fiberings $SF(M)$ is known to have contractible components. It is also known that the space of Hopf fiberings of the three-sphere is noncontractible. We provide the second example of a non-aspherical 3-manifold $M$ such that $SF(M)$ has noncontractible components. In particular, we show that certain components of $SF(S^1 \times S^2)$ are homotopy equivalent to a subspace homeomorphic to the identity-based loop space $ΩSO(3)$, and we exhibit second homology generators for both connected components of $SF(S^1 \times S^2)$. |
| title | On the homotopy type of the space of fiberings of $S^1 \times S^2$ by simple closed curves |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2404.08545 |