The tangent groupoid of a Heisenberg manifold
| dc.creator | Ponge, Raphael | |
| dc.date | 2004-04-07 | |
| dc.date | 2006-02-14 | |
| dc.date.accessioned | 2026-07-07T08:06:15Z | |
| dc.date.available | 2026-07-07T08:06:15Z | |
| dc.description | As a step toward proving an index theorem for hypoelliptic operators Heisenberg manifolds, including those on CR and contact manifolds, we construct an analogue for Heisenberg manifolds of Connes' tangent groupoid of a manifold $M$. As it is well known for a Heisenberg manifold $(M,H)$ the relevant notion of tangent is rather that of Lie group bundle of graded 2-step nilpotent Lie groups $GM$. We then construct the tangent groupoid of $(M,H)$ as a differentiable groupoid $\cG_{H} M$ encoding the smooth deformation of $M\times M$ to $GM$. In this construction a crucial use is made of a refined notion of privileged coordinates and of a tangent approximation result for Heisenberg diffeomorphisms. | |
| dc.description | v7: final version; to appear in Pacific Math. J.; 18 pages | |
| dc.identifier | https://arxiv.org/abs/math/0404174 | |
| dc.identifier | http://arxiv.org/abs/math/0404174 | |
| dc.identifier | Pacific J. Math. 227 (2006) 151-175 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130541 | |
| dc.subject | Differential Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | Operator Algebras | |
| dc.subject | Primary 58H05; Secondary 53C10, 53D10, 32V05 | |
| dc.title | The tangent groupoid of a Heisenberg manifold | |
| dc.type | text |