$\mathbb{Z}_2$-actions on positively curved manifolds
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914955743199232 |
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| author | Ghazawneh, Farida |
| author_facet | Ghazawneh, Farida |
| contents | Kennard, Khalili Samani, and Searle showed that for a $\mathbb{Z}_2$-torus acting on a closed, positively curved Riemannian $n$-manifold, $M^{n}$, with a non-empty fixed point set for $n$ large enough and $r$ approximately half the dimension of $M$, then $M^n$ is homotopy equivalent to $S^n$, $\mathbb{R}\mathrm{P}^{n}$, $\mathbb{C}\mathrm{P}^{\frac{n}{2}}$, or a lens space. In this paper, we lower $r$ to approximately $2n/5$ and show that we still obtain the same result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15392 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $\mathbb{Z}_2$-actions on positively curved manifolds Ghazawneh, Farida Differential Geometry 53C20, 57S25 Kennard, Khalili Samani, and Searle showed that for a $\mathbb{Z}_2$-torus acting on a closed, positively curved Riemannian $n$-manifold, $M^{n}$, with a non-empty fixed point set for $n$ large enough and $r$ approximately half the dimension of $M$, then $M^n$ is homotopy equivalent to $S^n$, $\mathbb{R}\mathrm{P}^{n}$, $\mathbb{C}\mathrm{P}^{\frac{n}{2}}$, or a lens space. In this paper, we lower $r$ to approximately $2n/5$ and show that we still obtain the same result. |
| title | $\mathbb{Z}_2$-actions on positively curved manifolds |
| topic | Differential Geometry 53C20, 57S25 |
| url | https://arxiv.org/abs/2409.15392 |