### Abstract

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 S^{3} 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.

Original language | English |
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Pages (from-to) | 487-495 |

Number of pages | 9 |

Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

Volume | 139 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2005 Nov 1 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Ishikawa, M. (2005). On the Thurston-Bennequin invariant of graph divide links.

*Mathematical Proceedings of the Cambridge Philosophical Society*,*139*(3), 487-495. https://doi.org/10.1017/S0305004105008741