[Sub-Riemannian Seminars] Raphael Ponge - The tangent groupoid of a Carnot manifold - Today, 16:00 CEST
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Enrico Le Donne enrico.ledonne@gmail.com via univ-grenoble-alpes.fr
7:18 PM (2 hours ago)
to Sub-Riemannian
Dear all,
This is a reminder for today's session of the "Sub-Riemannian
Seminars" (Fri Apr 23, 16:00-17:00 Paris time (CEST), on Zoom).
The speaker will be Raphael Ponge (Sichuan University), who will give
a talk with the title: "The tangent groupoid of a Carnot manifold. ".
Abstract: This talk will deal with the infinitesimal structure of
Carnot manifolds. By a Carnot manifold we mean a manifold together
with a subbundle filtration of its tangent bundle which is compatible
with the Lie bracket of vector fields. We introduce a notion of
differential, called Carnot differential, for Carnot manifolds maps
(i.e., maps that are compatible with the Carnot manifold structure).
This differential is obtained as a group map between the
corresponding tangent groups. We prove that, at every point, a Carnot
manifold map is osculated in a very precise way by its Carnot
differential at the point. We also show that, in the case of maps
between nilpotent graded groups, the Carnot differential is given by
the Pansu derivative. Therefore, the Carnot differential is the
natural generalization of the Pansu derivative to maps between general
Carnot manifolds. Another main result is the construction of an
analogue for Carnot manifolds of Connes' tangent groupoid. Given any
Carnot manifold $(M,H)$ we get a smooth groupoid that encodes the
smooth deformation of the pair $M\times M$ to the tangent group bundle
$GM$. This shows that, at every point, the tangent group is the
tangent space in a true differential-geometric fashion. Moreover, the
very fact that we have a groupoid accounts for the group structure of
the tangent group. Incidentally, this answers a well-known question of
Bellaiche. This is joint work with Woocheol Choi.
Direct Zoom link:
https://univ-grenoble-alpes-fr.zoom.us/j/99026386616?pwd=MmplbmdtNVVNazdtTExpVktYb2REdz09
On behalf of the organizers (Ugo Boscain, Enrico Le Donne, Luca Rizzi,
Mario Sigalotti, Emmanuel Trélat)
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