Tangent maps and tangent groupoid for Carnot manifolds

@article{Choi2015TangentMA,
  title={Tangent maps and tangent groupoid for Carnot manifolds},
  author={Woocheol Choi and Raphael Ponge},
  journal={Differential Geometry and its Applications},
  year={2015}
}
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20 Citations
Highly Influential Citations
1
Background Citations
5
Methods Citations
6

20 Citations

Privileged Coordinates and Nilpotent Approximation for Carnot Manifolds, II. Carnot Coordinates

This paper is a sequel of Choi and Ponge (J Dyn Control Syst 25:109–157, 2019) and deals with privileged coordinates and nilpotent approximation of Carnot manifolds. By a Carnot manifold, it is meant…

Privileged Coordinates and Nilpotent Approximation for Carnot Manifolds, II. Carnot Coordinates

This paper is a sequel of Choi and Ponge (J Dyn Control Syst 25:109–157, 2019) and deals with privileged coordinates and nilpotent approximation of Carnot manifolds. By a Carnot manifold, it is meant…

Privileged Coordinates and Nilpotent Approximation of Carnot Manifolds, I. General Results

In this paper, we attempt to give a systematic account on privileged coordinates and nilpotent approximation of Carnot manifolds. By a Carnot manifold, it is meant a manifold with a distinguished…

A transverse index theorem in the calculus of filtered manifolds

We use filtrations of the tangent bundle of a manifold starting with an integrable subbundle to define transverse symbols to the corresponding foliation, define a condition of transversally Rockland and…

Privileged Coordinates and Nilpotent Approximation of Carnot Manifolds, I. General Results

In this paper, we attempt to give a systematic account on privileged coordinates and nilpotent approximation of Carnot manifolds. By a Carnot manifold, it is meant a manifold with a distinguished…

Euler-Like Vector Fields, Deformation Spaces and Manifolds with Filtered Structure

The first purpose of this note is to comment on a recent article of Bursztyn, Lima and Meinrenken, in which it is proved that if M is a smooth submanifold of a manifold V, then there is a bijection…

Tangent groupoid and tangent cones in sub-Riemannian geometry

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…

The Heat Asymptotics on Filtered Manifolds

A universal heat kernel expansion for formally self-adjoint non-negative Rockland differential operators on general closed filtered manifolds is established and Weyl’s law for the eigenvalue asymptotics is described.

Pseudodifferential operators on filtered manifolds as generalized fixed points

On filtered manifolds one can define a different notion of order for the differential operators. In this paper, we use generalized fixed point algebras to construct a pseudodifferential extension…

A pseudodifferential calculus for maximally hypoelliptic operators and the Helffer-Nourrigat conjecture

We extend the classical regularity theorem of elliptic operators to maximally hypoelliptic differential operators. More precisely, given vector fields X1, . . . , Xm on a smooth manifold which…

References

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Privileged Coordinates and Nilpotent Approximation for Carnot Manifolds, II. Carnot Coordinates

This paper is a sequel of Choi and Ponge (J Dyn Control Syst 25:109–157, 2019) and deals with privileged coordinates and nilpotent approximation of Carnot manifolds. By a Carnot manifold, it is meant…

Privileged Coordinates and Nilpotent Approximation of Carnot Manifolds, I. General Results

In this paper, we attempt to give a systematic account on privileged coordinates and nilpotent approximation of Carnot manifolds. By a Carnot manifold, it is meant a manifold with a distinguished…

On Carnot-Carathéodory metrics

Consider a smooth Riemannian ^-manifold (M, g) equipped with a smooth distribution of /c-planes. Such a distribution Δ assigns to each point m e M a /^-dimensional subspace of the tangent space TmM.…

The tangent grupoid of a Heisenberg manifold

As a step towards proving an index theorem for hypoelliptic operators on Heisenberg manifolds, including for those on CR and contact manifolds, we construct an analogue for Heisenberg manifolds of…

The Geometry of the Osculating Nilpotent Group Structures of the Heisenberg Calculus

We explore the geometry that underlies the osculating nilpotent group structures of the Heisenberg calculus. For a smooth manifold $M$ with a distribution $H\subseteq TM$ analysts use explicit (and…

Sub-riemannian geometry from intrinsic viewpoint

Gromov proposed to extract the (di erential) geometric content of a sub-riemannian space exclusively from its Carnot-Carath eodory distance. One of the most striking features of a regular…

The differential of a quasi-conformal mapping of a Carnot-Caratheodory space

The theory of quasi-conformal mappings has been used to prove rigidity theorems on hyperbolic n space over the division algebras ℝ, ℂ, ℍ, and \({\Bbb O}\), by studying quasi-conformal mappings on…

The Atiyah-Singer index formula for subelliptic operators on contact manifolds. Part I

The Atiyah-Singer index theorem gives a topological formula for the index of an elliptic differential operator. The topological index depends on a cohomology class that is constructed from the…

Euler-Like Vector Fields, Deformation Spaces and Manifolds with Filtered Structure

The first purpose of this note is to comment on a recent article of Bursztyn, Lima and Meinrenken, in which it is proved that if M is a smooth submanifold of a manifold V, then there is a bijection…

Fourier integrals operators on lie groupoids

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