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A G-version of Smale's theorem | | Imre Major
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15 Dec 2001 | | Subject: | Differential Geometry; Group Theory MSC-class: 57M70 | math.DG math.GR | | Abstract: | 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 $epsilon>0$ 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 | | Source: | arXiv, math.DG/0201133 | | Services: | Forum | Review | PDF | Favorites | |
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