Ozsváth-Szabó invariants and tight contact three-manifolds, II

By P. Lisca, A. Stipsicz. 2004

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Let S 3 (K) be the oriented 3{manifold obtained by rational r{surgery on a knot K S 3 . Using the contact Ozsv ath{Szab o invariants we prove, for a class of knots K containing all the algebraic knots, that S 3 (K) carries positive, tight contact structures for every r 6 g s ( K ) 1, where gs(K) is the slice genus of K . This implies, in particular, that the Brieskorn spheres (2; 3; 4) and (2; 3; 3) carry tight, positive contact structures. As an application of our main result we show that for each m2N there exists a Seifert bered rational homology 3{sphere Mm carrying at least m pairwise non{isomorphic tight, nonllable contact structures.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4d0af450e9c48dcba4bf7a4d805f5487e837fe53

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Citations in the corpus

Twisting quasi-alternating links (2007, background): “According to [8, 12 ], for the pretzel link L = P(p1,p2, −q) with p1,p2,q ≥ 2, �(L) is an L–space if and only if”
Ozsvth-Szab invariants and tight contact 3-manifolds, III (2007, background): “In this latter case, the idea used in [24] does not work, since it would require the application of contact 0-surgery, which automatically leads to overtwisted structures.”
Planar open books and Floer homology (2005, methodology): “In another direction, it forms the foundations for the “contact invariant” in Heegaard Floer homology [20], a tool which has been helpful in the classification of contact structures over certain 3–manifolds [15, 16].”
Handle moves in contact surgery diagrams (2008, background): “The resulting contact surgery diagrams were studied more carefully in [6] and since then have led — in particular, when combined with Heegaard Floer theory — to a wealth of applications; see, for example, [17], [26], [31].”
Involutive Heegaard Floer homology (2015, methodology): “HF(Y;s) ˘= ! HF(Y;s) for any spinc structure s on Y. We have J2 = id, so Jis an involution on HF(Y):This involution was used in various arguments in the Heegaard Floer literature; see for example [21, 20]. We dene involutive Heegaard Floer homology by making use of the construction of J at the chain”