# Tangent groupoid and tangent cones in sub-Riemannian geometry

@inproceedings{Mohsen2022TangentGA, title={Tangent groupoid and tangent cones in sub-Riemannian geometry}, author={Omar Mohsen}, year={2022} }

Let X 1 , ¨ ¨ ¨ , X m be vector ﬁelds satisfying Hörmander’s Lie bracket generating condition on a smooth manifold M . We generalise Connes’s tangent groupoid, by constructing a com-pletion of the space M ˆ M ˆ R ˆ` using the sub-Riemannian metric. We use our space to calculate all the tangent cones of the sub-Riemannian metric in the sense of the Gromov-Hausdorﬀ distance. This generalises a result of Bellaïche.

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