Ozsath-Szabo invariants and tight contact three-manifolds, I

Let S-r(3)(K) be the oriented 3-manifold obtained by rational r-surgery on a knot K subset of S-3. Using the contact Ozsvath-Szabo invariants we prove, for a class of knots K containing all the algebraic knots, that S-r(3)(K) carries positive, tight contact structures for every r not equal 2g(s)( K)-1, where g(s)(K) is the slice genus of K. This implies, in particular, that the Brieskorn spheres -Sigma(2; 3; 4) and -Sigma( 2; 3; 3) carry tight, positive contact structures. As an application of our main result we show that for each m is an element of N there exists a Seifert fibered rational homology 3-sphere M-m carrying at least m pairwise non-isomorphic tight, nonfillable contact structures.