We determine the Thurston-Bennequin invariant of graph divide links, which include all closed positive braids, all divide links and certain negative twist knots. As a corollary of this and a result of P. Lisca and A. I. Stipsicz, we prove that the 3-manifold obtained from S3 by Dehn surgery along a non-trivial graph divide knot K with coefficient r carries positive, tight contact structures for every r except the Thurston-Bennequin invariant of K.
|Number of pages||9|
|Journal||Mathematical Proceedings of the Cambridge Philosophical Society|
|Publication status||Published - 2005 Nov 1|
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