Abstract
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.
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