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Surgeries of index one and isotopies of spheres in tight contact manifolds. (Chirurgies d’indice un et isotopies de sphères dans les variétés de contact tendues.) (French. Abridged English version) Zbl 0876.57051

Summary: We prove the following theorems:
(1) Any surgery of index one on a tight contact manifold (of dimension three) gives rise to a manifold which carries a natural tight contact structure.
(2) In a tight contact manifold, any two isotopic spheres which carry the same characteristic foliation are isotopic through a contact isotopy.
(3) In a tight contact manifold, any two isotopic spheres have isomorphic complements.

MSC:

57R65 Surgery and handlebodies
57M50 General geometric structures on low-dimensional manifolds
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