Abnormal Singular Foliations and the Sard Conjecture for generic co-rank one distributions
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913879396712448 |
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| author | da Silva, A Belotto Parusiński, A Rifford, L |
| author_facet | da Silva, A Belotto Parusiński, A Rifford, L |
| contents | Given a smooth totally nonholonomic distribution on a smooth manifold, we construct a singular distribution capturing essential abnormal lifts which is locally generated by vector fields with controlled divergence. Then, as an application, we prove the Sard Conjecture for rank 3 distribution in dimension 4 and generic distributions of corank 1. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_20284 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Abnormal Singular Foliations and the Sard Conjecture for generic co-rank one distributions da Silva, A Belotto Parusiński, A Rifford, L Differential Geometry Given a smooth totally nonholonomic distribution on a smooth manifold, we construct a singular distribution capturing essential abnormal lifts which is locally generated by vector fields with controlled divergence. Then, as an application, we prove the Sard Conjecture for rank 3 distribution in dimension 4 and generic distributions of corank 1. |
| title | Abnormal Singular Foliations and the Sard Conjecture for generic co-rank one distributions |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2310.20284 |