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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2512.23101 |
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| _version_ | 1866912793457852416 |
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| author | Mendes, Ricardo Minuzzo, Alessandro Radeschi, Marco |
| author_facet | Mendes, Ricardo Minuzzo, Alessandro Radeschi, Marco |
| contents | We prove that a compact simply connected manifold $M$ with a variationally complete $G$-action satisfying certain mild conditions (e.g. trivial principal isotropy, or simply connected principal orbits) is rationally elliptic if and only if $M/G$ is flat. This answers several conjectures and problems regarding the rational homotopy of manifolds with symmetries. On the other hand, without the extra conditions we find examples of rationally elliptic $G$-manifolds $M$ where $M/G$ admits a hyperbolic metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23101 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Rational Hyperbolicity problem Mendes, Ricardo Minuzzo, Alessandro Radeschi, Marco Differential Geometry We prove that a compact simply connected manifold $M$ with a variationally complete $G$-action satisfying certain mild conditions (e.g. trivial principal isotropy, or simply connected principal orbits) is rationally elliptic if and only if $M/G$ is flat. This answers several conjectures and problems regarding the rational homotopy of manifolds with symmetries. On the other hand, without the extra conditions we find examples of rationally elliptic $G$-manifolds $M$ where $M/G$ admits a hyperbolic metric. |
| title | On the Rational Hyperbolicity problem |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2512.23101 |