On circle actions with exactly three fixed points
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908738603974656 |
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| author | Wiemeler, Michael |
| author_facet | Wiemeler, Michael |
| contents | We study smooth, closed orientable $S^1$-manifolds $M$ with exactly $3$ fixed points. We show that the dimension of $M$ is of the form $4\cdot 2^a$ or $8\cdot(2^a+2^b)$ with $a,b\geq 0$ and $a\neq b$. Moreover, under the extra assumption that $M$ is spin or unitary we determine exactly the dimension of $M$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_15396 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On circle actions with exactly three fixed points Wiemeler, Michael Geometric Topology Differential Geometry 57S15, 57R15, 57R20, 57R85, 55N91 We study smooth, closed orientable $S^1$-manifolds $M$ with exactly $3$ fixed points. We show that the dimension of $M$ is of the form $4\cdot 2^a$ or $8\cdot(2^a+2^b)$ with $a,b\geq 0$ and $a\neq b$. Moreover, under the extra assumption that $M$ is spin or unitary we determine exactly the dimension of $M$. |
| title | On circle actions with exactly three fixed points |
| topic | Geometric Topology Differential Geometry 57S15, 57R15, 57R20, 57R85, 55N91 |
| url | https://arxiv.org/abs/2303.15396 |