Smooth contact lifts to central extensions of Carnot groups
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arXiv
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| Format: | Preprint |
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2025
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| author | Hakavuori, Eero Heikkilä, Susanna Ikonen, Toni |
| author_facet | Hakavuori, Eero Heikkilä, Susanna Ikonen, Toni |
| contents | We consider the existence problem of lifting a smooth contact map between Carnot groups to a smooth contact map between central extensions of the original groups. Our main result is a necessary and sufficient criterion formulated using the pullback of any de Rham potential of the codomain central extension 2-cocycle: the Rumin differential of the pullback is in a linear image of the domain central extension 2-cocycle. We also show a necessary criterion using the Pansu pullback: the Pansu pullback of the codomain central extension 2-cocycle and a linear image of the domain central extension 2-cocycle are in the same Lie algebra cohomology class. We prove that the latter criterion is sufficient if the domain group is Lipschitz 1-connected, or if the pullback has maximal weight among Lie algebra 2-cohomology classes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_14647 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Smooth contact lifts to central extensions of Carnot groups Hakavuori, Eero Heikkilä, Susanna Ikonen, Toni Differential Geometry Metric Geometry Primary: 35R03. Secondary: 20F65, 22E30, 53C17, 53C24, 57T10 We consider the existence problem of lifting a smooth contact map between Carnot groups to a smooth contact map between central extensions of the original groups. Our main result is a necessary and sufficient criterion formulated using the pullback of any de Rham potential of the codomain central extension 2-cocycle: the Rumin differential of the pullback is in a linear image of the domain central extension 2-cocycle. We also show a necessary criterion using the Pansu pullback: the Pansu pullback of the codomain central extension 2-cocycle and a linear image of the domain central extension 2-cocycle are in the same Lie algebra cohomology class. We prove that the latter criterion is sufficient if the domain group is Lipschitz 1-connected, or if the pullback has maximal weight among Lie algebra 2-cohomology classes. |
| title | Smooth contact lifts to central extensions of Carnot groups |
| topic | Differential Geometry Metric Geometry Primary: 35R03. Secondary: 20F65, 22E30, 53C17, 53C24, 57T10 |
| url | https://arxiv.org/abs/2508.14647 |