BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Raphael Ponge (Sichuan University) DTSTART:20210423T140000Z DTEND:20210423T150000Z DTSTAMP:20260423T035754Z UID:SRS/13 DESCRIPTION:Title: The tangent groupoid of a Carnot manifold\nby Raphael Ponge (Sichuan Univ ersity) as part of Sub-Riemannian Seminars\n\n\nAbstract\nThis talk will d eal with the infinitesimal structure of Carnot manifolds. By a Carnot mani fold we mean a manifold together with a subbundle filtration of its tangen t bundle which is compatible with the Lie bracket of vector fields. We int roduce a notion of differential\, called Carnot differential\, for Carnot manifolds maps (i.e.\, maps that are compatible with the Carnot manifold s tructure). This differential is obtained as a group map between the corre sponding tangent groups. We prove that\, at every point\, a Carnot manifol d 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 g roups\, the Carnot differential is given by the Pansu derivative. Therefor e\, the Carnot differential is the natural generalization of the Pansu der ivative to maps between general Carnot manifolds. Another main result is a construction of an analogue for Carnot manifolds of Connes' tangent group oid. Given any Carnot manifold $(M\,H)$ we get a smooth groupoid that enco des the smooth deformation of the pair $M\\times M$ to the tangent group b undle $GM$. This shows that\, at every point\, the tangent group is the t angent space in a true differential-geometric fashion. Moreover\, the very fact that we have a groupoid accounts for the group structure of the tang ent group. Incidentally\, this answers a well-known question of Bellaiche. This is joint work with Woocheol Choi.\n LOCATION:https://researchseminars.org/talk/SRS/13/ END:VEVENT END:VCALENDAR