Tight contact structures of certain Seifert fibered 3-manifolds with e(0)=-1

Abstract

We classify, up to contact isotopy, all tight contact structures on a family of Seifert fibered three-manifolds M(-1/2, 1/3, beta/alpha) satisfying 0 < beta/alpha < 1/6. We show that, if [r(0), r(1),..., r(l)] is the continued fraction expansion of -alpha/beta, there are exactly |r(0)+ 5| |r(1)+ 1| center dot center dot center dot | r(l)+ 1| tight contact structures on such Seifert fibered three-manifolds M -1/2, 1/3, beta/alpha) as above, so all the tight contact structures are holomorphically fillable.