Group Extensions and Principal Fibrations.
Une homotopie régulière , , dans une variété symplectique est dite inactive si en chaque point le déplacement infinitésimal est -orthogonal à l’espace tangent de l’objet déplacé. Si est un polyèdre de de dimension et si est un ouvert de , toute homotopie de jusqu’à est déformable en une homotopie régulière inactive. On donne une application à l’engouffrement en géométrie symplectique.
We show that if X, Y are smooth, compact k-dimensional submanifolds of ℝⁿ and 2k+2 ≤ n, then each diffeomorphism ϕ: X → Y can be extended to a diffeomorphism Φ: ℝⁿ → ℝⁿ which is tame (to be defined in this paper). Moreover, if X, Y are real analytic manifolds and the mapping ϕ is analytic, then we can choose Φ to be also analytic. We extend this result to some interesting categories of closed (not necessarily compact) subsets of ℝⁿ, namely, to the category of Nash submanifolds...
We construct closed complex submanifolds of which are differential but not holomorphic complete intersections. We also prove a homotopy principle concerning the removal of intersections with certain complex subvarieties of .