The holonomy Lie $\infty$-groupoid of a singular foliation I
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917323310366720 |
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| author | Laurent-Gengoux, Camille Louis, Ruben |
| author_facet | Laurent-Gengoux, Camille Louis, Ruben |
| contents | We construct a finite-dimensional higher Lie groupoid integrating a singular foliation $\mathcal{F}$, under the mild assumption that the latter admits a geometric resolution. More precisely, a recursive use of bi-submersions, a tool coming from non-commutative geometry and invented by Androulidakis and Skandalis, allows us to integrate any universal Lie $ \infty$-algebroid of a singular foliation to a Kan simplicial manifold, where all components are made of non-connected manifolds which are all the same finite dimension that can be chosen to be equal to the ranks of a given geometric resolution. Its $1$-truncation is the Androulidakis-Skandalis holonomy groupoid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23871 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The holonomy Lie $\infty$-groupoid of a singular foliation I Laurent-Gengoux, Camille Louis, Ruben Category Theory Differential Geometry We construct a finite-dimensional higher Lie groupoid integrating a singular foliation $\mathcal{F}$, under the mild assumption that the latter admits a geometric resolution. More precisely, a recursive use of bi-submersions, a tool coming from non-commutative geometry and invented by Androulidakis and Skandalis, allows us to integrate any universal Lie $ \infty$-algebroid of a singular foliation to a Kan simplicial manifold, where all components are made of non-connected manifolds which are all the same finite dimension that can be chosen to be equal to the ranks of a given geometric resolution. Its $1$-truncation is the Androulidakis-Skandalis holonomy groupoid. |
| title | The holonomy Lie $\infty$-groupoid of a singular foliation I |
| topic | Category Theory Differential Geometry |
| url | https://arxiv.org/abs/2503.23871 |