A G-version of Smale's theorem
| dc.creator | Major, Imre | |
| dc.date | 2002-01-15 | |
| dc.date.accessioned | 2026-07-07T04:45:52Z | |
| dc.date.available | 2026-07-07T04:45:52Z | |
| dc.description | We will prove the equivariant version of Smale's transversality theorem: suppose that the compact Lie-group G acts on the compact differentiable manifold M on which an invariant Morse-function f and an invariant vector field X are given so that X is gradient-like with respect to f (i.e. X(f)<0 away from critical orbits and X is the gradient of f (w.r.t. a fixed invariant Riemannian metric) on some invariant open subsets about critical orbits of f.) Given a bound $ε>0$ we will prove the existence of an invariant vector field Y of class C^1 for which vector field X+Y is also gradient-like such that: (a) |Y|_1<ε(here |.|_1 is the C^1 norm). (b)The intersection of the stable and unstable sets of vector field X+Y taken at a pair of critical orbits of f is transverse when restricted to an orbit type of the action. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0201133 | |
| dc.identifier | http://arxiv.org/abs/math/0201133 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63118 | |
| dc.subject | Differential Geometry | |
| dc.subject | Group Theory | |
| dc.subject | 57M70 | |
| dc.title | A G-version of Smale's theorem | |
| dc.type | text |