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arXiv · 2508.14647

Smooth contact lifts to central extensions of Carnot groups

Eero Hakavuori·Susanna Heikkilä·Toni Ikonen
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Abstract

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.

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Eero Hakavuori, Susanna Heikkilä, Toni Ikonen. 2025-08-20. Smooth contact lifts to central extensions of Carnot groups. https://arxiv.org/abs/2508.14647

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