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Homotopie régulière inactive et engouffrement symplectique

François Laudenbach (1986)

Annales de l'institut Fourier

Une homotopie régulière ϕ t : Δ ( M , ω ) , t [ 0 , 1 ] , dans une variété symplectique est dite inactive si en chaque point le déplacement infinitésimal est ω -orthogonal à l’espace tangent de l’objet déplacé. Si Δ est un polyèdre de M 2 n de dimension < n et si U est un ouvert de M , toute homotopie de Δ M jusqu’à Δ U est déformable en une homotopie régulière inactive. On donne une application à l’engouffrement en géométrie symplectique.

Link cobordism.

Sylvain E. Cappell, Julius L. Shaneson (1980)

Commentarii mathematici Helvetici

Manifolds with a unique embedding

Zbigniew Jelonek (2009)

Colloquium Mathematicae

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...

On complete intersections

Franc Forstnerič (2001)

Annales de l’institut Fourier

We construct closed complex submanifolds of n which are differential but not holomorphic complete intersections. We also prove a homotopy principle concerning the removal of intersections with certain complex subvarieties of n .

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