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On the Thurston–Bennequin invariant of graph divide links

Published online by Cambridge University Press:  21 October 2005

MASAHARU ISHIKAWA
MASAHARU ISHIKAWA
Affiliation:
Department of Mathematics, Tokyo Institute of Technology, 2-12-1, Oh-okayama, Meguro-ku, Tokyo, 152-8551, Japan. e-mail: ishikawa@math.titech.ac.jp
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 139 , Issue 3 , November 2005 , pp. 487 - 495
Copyright
2005 Cambridge Philosophical Society

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