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Recollement de variétés de contact tendues. (Gluing tight contact manifolds.). (French) Zbl 0930.53053

Bull. Soc. Math. Fr. 127, No. 1, 43-69 (1999); addendum ibid. 127, 623 (1999).
Author’s abstract: “We study the behaviour of tight contact structures under surgery operations along disks and tori. The main result says that if one glues two tight contact manifolds along incompressible tori, the resulting manifold is tight provided that the original structures are universally tight and that the tori are quasi pre-Lagrangian (for instance, this is the case if \(\xi\) induces on the tori a foliation by circles). Moreover, we construct an example which shows that without this last assumption, the new manifold can be overtwisted. As an application of these techniques, using a recent theorem of Y. M. Eliashberg and W. P. Thurston [‘Confoliations’ (Univ. Lect. Ser. 13, AMS, Providence) (1998; Zbl 0893.53001)], we construct a tight contact structure on “almost” every graph manifold and on a new class of toroidal homology spheres”.
Reviewer: D.Perrone (Lecce)

MSC:

53D35 Global theory of symplectic and contact manifolds
57R17 Symplectic and contact topology in high or arbitrary dimension
53D10 Contact manifolds (general theory)
57R65 Surgery and handlebodies

Citations:

Zbl 0893.53001
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References:

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