A-Foliations of codimension two on compact simply-connected manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866912786783666176 |
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| author | Corro, Diego |
| author_facet | Corro, Diego |
| contents | We show that a singular Riemannian foliation of codimension two on a compact simply-connected Riemannian $(n+2)$-manifold, with regular leaves homeomorphic to the $n$-torus, is given by a smooth effective $n$-torus action. This solves in the negative for the codimension $2$ case a question about the existence of foliations by exotic tori on simply-connected manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1903_07191 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | A-Foliations of codimension two on compact simply-connected manifolds Corro, Diego Differential Geometry 53C12, 57R30, 53C24 We show that a singular Riemannian foliation of codimension two on a compact simply-connected Riemannian $(n+2)$-manifold, with regular leaves homeomorphic to the $n$-torus, is given by a smooth effective $n$-torus action. This solves in the negative for the codimension $2$ case a question about the existence of foliations by exotic tori on simply-connected manifolds. |
| title | A-Foliations of codimension two on compact simply-connected manifolds |
| topic | Differential Geometry 53C12, 57R30, 53C24 |
| url | https://arxiv.org/abs/1903.07191 |