• Corpus ID: 254247087

Tangent groupoid and tangent cones in sub-Riemannian geometry

  title={Tangent groupoid and tangent cones in sub-Riemannian geometry},
  author={Omar Mohsen},
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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