### 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 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**On the Thurston-Bennequin invariant of graph divide links.** / Ishikawa, Masaharu.

Research output: Contribution to journal › Article

*Mathematical Proceedings of the Cambridge Philosophical Society*, vol. 139, no. 3, pp. 487-495. https://doi.org/10.1017/S0305004105008741

}

TY - JOUR

T1 - On the Thurston-Bennequin invariant of graph divide links

AU - Ishikawa, Masaharu

PY - 2005/11/1

Y1 - 2005/11/1

N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=27244459293&partnerID=8YFLogxK

U2 - 10.1017/S0305004105008741

DO - 10.1017/S0305004105008741

M3 - Article

VL - 139

SP - 487

EP - 495

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

IS - 3

ER -