The diffeomorphism group of a Lie foliation
| dc.creator | Hector, G. | |
| dc.creator | Macías-Virgós, E. | |
| dc.creator | Sotelo-Armesto, A. | |
| dc.date | 2008-12-13 | |
| dc.date.accessioned | 2026-07-07T12:12:42Z | |
| dc.date.available | 2026-07-07T12:12:42Z | |
| dc.description | We explicitly compute the diffeomorphism group of several types of linear foliations (with dense leaves) on the torus $T^n$, $n\geq 2$, namely codimension one foliations, flows, and the so-called non-quadratic foliations. We show in particular that non-quadratic foliations are rigid, in the sense that they do not admit transverse diffeomorphisms other than $\pm \id$ and translations. The computation is an application of a general formula that we prove for the diffeomorphism group of any Lie foliation with dense leaves on a compact manifold. Our results generalize those of P. Donato and P. Iglesias for $T^2$, P. Iglesias and G. Lachaud for codimension one foliations on $T^n$, $n\geq 2$, and B. Herrera for transcendent foliations. The theoretical setting of the paper is that of J. M. Souriau's diffeological spaces. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/0812.2550 | |
| dc.identifier | http://arxiv.org/abs/0812.2550 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/210629 | |
| dc.subject | Differential Geometry | |
| dc.subject | 57R30, 22E65, 58D05, 58B25 | |
| dc.title | The diffeomorphism group of a Lie foliation | |
| dc.type | text |