Rational ellipticity of $G$-manifolds from their quotients
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912164292329472 |
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| author | Samani, Elahe Khalili Radeschi, Marco |
| author_facet | Samani, Elahe Khalili Radeschi, Marco |
| contents | We prove that if a compact, simply connected Riemannian $G$-manifold $M$ has orbit space $M/G$ isometric to some other quotient $N/H$ with $N$ having zero topological entropy, then $M$ is rationally elliptic. This result, which generalizes most conditions on rational ellipticity, is a particular case of a more general result involving manifold submetries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_08202 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rational ellipticity of $G$-manifolds from their quotients Samani, Elahe Khalili Radeschi, Marco Differential Geometry 53C21 (Primary) 53C12 (Secondary) We prove that if a compact, simply connected Riemannian $G$-manifold $M$ has orbit space $M/G$ isometric to some other quotient $N/H$ with $N$ having zero topological entropy, then $M$ is rationally elliptic. This result, which generalizes most conditions on rational ellipticity, is a particular case of a more general result involving manifold submetries. |
| title | Rational ellipticity of $G$-manifolds from their quotients |
| topic | Differential Geometry 53C21 (Primary) 53C12 (Secondary) |
| url | https://arxiv.org/abs/2312.08202 |