Circle actions and Suspension operations on Smooth manifolds
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866908984159502336 |
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| author | Duan, Haibao |
| author_facet | Duan, Haibao |
| contents | Let $M$ be a smooth manifold with $\dim M\geq 3$ and a base point $x_{0}$. Surgeries along the oriented circle $S^{1}\times \{x_{0}\}$ on the product $ S^{1}\times M$ yields two manifolds $Σ_{0}M$ and $Σ_{1}M$, called the suspensions of $M$.
The suspension operations $Σ_{i}$ play a basic role in the construction and classification of the smooth manifolds which admit free $ S^{1}$-actions. We illustrate this by a number of applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_06225 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Circle actions and Suspension operations on Smooth manifolds Duan, Haibao Geometric Topology Algebraic Topology 57R65, 57M60, 55N45 Let $M$ be a smooth manifold with $\dim M\geq 3$ and a base point $x_{0}$. Surgeries along the oriented circle $S^{1}\times \{x_{0}\}$ on the product $ S^{1}\times M$ yields two manifolds $Σ_{0}M$ and $Σ_{1}M$, called the suspensions of $M$. The suspension operations $Σ_{i}$ play a basic role in the construction and classification of the smooth manifolds which admit free $ S^{1}$-actions. We illustrate this by a number of applications. |
| title | Circle actions and Suspension operations on Smooth manifolds |
| topic | Geometric Topology Algebraic Topology 57R65, 57M60, 55N45 |
| url | https://arxiv.org/abs/2202.06225 |