Stability of compact actions of the Heisenberg group
| dc.creator | Begazo, Tania M. | |
| dc.creator | Saldanha, Nicolau C. | |
| dc.date | 2004-12-27 | |
| dc.date | 2005-07-22 | |
| dc.date.accessioned | 2026-07-07T05:15:40Z | |
| dc.date.available | 2026-07-07T05:15:40Z | |
| dc.description | Let G be the Heisenberg group of real lower triangular 3x3 matrices with unit diagonal. A locally free smooth action of G on a manifold M^4 is given by linearly independent vector fields X_1, X_2, X_3 such that X_3 = [X_1,X_2] and [X_1,X_3] = [X_2, X_3] = 0. The C^1 topology for vector fields induces a topology in the space of actions of G on M^4. An action is compact if all orbits are compact. Given a compact action $θ$, we investigate under which conditions its C^1 perturbations $\tildeθ$ are guaranteed to be compact. There is more than one interesting definition of stability, and we show that in the case of the Heisenberg group, unlike for actions of R^n, the definitions do not turn out to be equivalent. | |
| dc.description | 17 pages, no figures (corrected typos and added references) | |
| dc.identifier | https://arxiv.org/abs/math/0412501 | |
| dc.identifier | http://arxiv.org/abs/math/0412501 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73705 | |
| dc.subject | Geometric Topology | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37C85; 57R30; 57M60 | |
| dc.title | Stability of compact actions of the Heisenberg group | |
| dc.type | text |