$\mathbb{Z}_2$-actions on positively curved manifolds

Fuente: arXiv
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Autore principale: Ghazawneh, Farida
Natura: Preprint
Pubblicazione: 2024
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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