Abstract
Let be the oriented 3–manifold obtained by rational –surgery on a knot . Using the contact Ozsváth–Szabó invariants we prove, for a class of knots containing all the algebraic knots, that carries positive, tight contact structures for every , where is the slice genus of . This implies, in particular, that the Brieskorn spheres and carry tight, positive contact structures. As an application of our main result we show that for each there exists a Seifert fibered rational homology 3–sphere carrying at least pairwise non–isomorphic tight, nonfillable contact structures.
Citation
Paolo Lisca. András I Stipsicz. "Ozsváth–Szábo invariants and tight contact three-manifolds I." Geom. Topol. 8 (2) 925 - 945, 2004. https://doi.org/10.2140/gt.2004.8.925
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