Blown-up singular Riemannian foliations
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917346535276544 |
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| author | Caramello Jr., Francisco C. Santos, Laura Ribeiro dos |
| author_facet | Caramello Jr., Francisco C. Santos, Laura Ribeiro dos |
| contents | In this paper we investigate new applications of the blow-up desingularization method in the context of singular Riemannian foliations. First, we relate the dynamics of such a foliation, which is governed by the so-called Molino sheaf, with that of its blow-up. In the particular case of singular Killing foliations, this leads to a strong constraint: the leaves of such foliations are all closed, provided the Euler characteristic of the ambient manifold is non-vanishing and its singular strata are all odd-codimensional. Next, we show that the space of leaf closures of a singular Killing foliation is the Gromov--Hausdorff limit of a sequence of orbifolds, whose dimensions are the codimension of the foliation. Finally, we relate the basic cohomology of a singular Riemannian foliation with that of its blow-up, generalizing well-known, classical analogous results in algebraic and complex geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07069 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Blown-up singular Riemannian foliations Caramello Jr., Francisco C. Santos, Laura Ribeiro dos Differential Geometry 53C12, 57R30 In this paper we investigate new applications of the blow-up desingularization method in the context of singular Riemannian foliations. First, we relate the dynamics of such a foliation, which is governed by the so-called Molino sheaf, with that of its blow-up. In the particular case of singular Killing foliations, this leads to a strong constraint: the leaves of such foliations are all closed, provided the Euler characteristic of the ambient manifold is non-vanishing and its singular strata are all odd-codimensional. Next, we show that the space of leaf closures of a singular Killing foliation is the Gromov--Hausdorff limit of a sequence of orbifolds, whose dimensions are the codimension of the foliation. Finally, we relate the basic cohomology of a singular Riemannian foliation with that of its blow-up, generalizing well-known, classical analogous results in algebraic and complex geometry. |
| title | Blown-up singular Riemannian foliations |
| topic | Differential Geometry 53C12, 57R30 |
| url | https://arxiv.org/abs/2512.07069 |