Rigidity of Nilpotent Lie Foliations: Cohomological Obstructions and Classification
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915864539824128 |
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| author | Ndiaye, Ameth |
| author_facet | Ndiaye, Ameth |
| contents | In this article, we develop a systematic cohomological framework for the study of the rigidity of nilpotent Lie foliations with respect to solvable deformations. We introduce the deformation complex associated to a pair of Lie algebras $(\mathfrak{g}, \mathfrak{h})$ and show that the main obstruction to deforming a nilpotent Lie foliation into a non-nilpotent solvable foliation lies in the cohomology group $H^2(\mathfrak{g},\mathfrak{g}/[\mathfrak{g},\mathfrak{g}])$. We establish a necessary and sufficient algebraic criterion for rigidity within the family of foliations modelled on the generalized Heisenberg groups $H_{2k+1}$. This result unifies and generalizes the construction of Dathe--Ndiaye (2012) as well as its subsequent extensions. We complete the article with a full classification of nilpotent Lie foliations of codimension at most six according to their deformation behaviour. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14415 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rigidity of Nilpotent Lie Foliations: Cohomological Obstructions and Classification Ndiaye, Ameth Differential Geometry In this article, we develop a systematic cohomological framework for the study of the rigidity of nilpotent Lie foliations with respect to solvable deformations. We introduce the deformation complex associated to a pair of Lie algebras $(\mathfrak{g}, \mathfrak{h})$ and show that the main obstruction to deforming a nilpotent Lie foliation into a non-nilpotent solvable foliation lies in the cohomology group $H^2(\mathfrak{g},\mathfrak{g}/[\mathfrak{g},\mathfrak{g}])$. We establish a necessary and sufficient algebraic criterion for rigidity within the family of foliations modelled on the generalized Heisenberg groups $H_{2k+1}$. This result unifies and generalizes the construction of Dathe--Ndiaye (2012) as well as its subsequent extensions. We complete the article with a full classification of nilpotent Lie foliations of codimension at most six according to their deformation behaviour. |
| title | Rigidity of Nilpotent Lie Foliations: Cohomological Obstructions and Classification |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2603.14415 |