On singular foliations tangent to a given hypersurface
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914670908014592 |
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| author | Francis, Michael |
| author_facet | Francis, Michael |
| contents | We consider a class of singular foliations in the sense of Androulidakis and Skandalis that we call transverse order $k$ foliations. These have a finite number of leaves: one hypersurface (the singular leaf) together with the components of its complement (open leaves). The positive integer parameter $k$ encodes the "order of tangency" of the leafwise vector fields to $L$. We show that a loop in the singular leaf induces a well-defined holonomy transformation at the level of $(k-1)$-jets. The resulting holonomy invariant can be used to give a complete classification of these foliations and obtain concrete descriptions of their associated groupoids and algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_03940 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On singular foliations tangent to a given hypersurface Francis, Michael Operator Algebras Differential Geometry 46L87, 53C12, 22A22 We consider a class of singular foliations in the sense of Androulidakis and Skandalis that we call transverse order $k$ foliations. These have a finite number of leaves: one hypersurface (the singular leaf) together with the components of its complement (open leaves). The positive integer parameter $k$ encodes the "order of tangency" of the leafwise vector fields to $L$. We show that a loop in the singular leaf induces a well-defined holonomy transformation at the level of $(k-1)$-jets. The resulting holonomy invariant can be used to give a complete classification of these foliations and obtain concrete descriptions of their associated groupoids and algebras. |
| title | On singular foliations tangent to a given hypersurface |
| topic | Operator Algebras Differential Geometry 46L87, 53C12, 22A22 |
| url | https://arxiv.org/abs/2311.03940 |