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On the transverse invariant for bindings of open books

David Shea Vela–Vick Columbia University

Differential Geometry mathscidoc:1609.10232

Journal of Differential Geometry, 88, (3), 533-552, 2011
Let T  (Y, ) be a transverse knot which is the binding of some open book, (T, ), for the ambient contact manifold (Y, ). In this paper, we show that the transverse invariant bT(T ) 2[HFK(−Y,K), defined in [LOSSz09], is nonvanishing for such transverse knots. This is true regardless of whether or not  is tight. We also prove a vanishing theorem for the invariants L and T. As a corollary, we show that if (T, ) is an open book with connected binding, then the complement of T has no Giroux torsion.
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@inproceedings{david2011on,
  title={ON THE TRANSVERSE INVARIANT FOR BINDINGS OF OPEN BOOKS},
  author={David Shea Vela–Vick},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913205337475781893},
  booktitle={Journal of Differential Geometry},
  volume={88},
  number={3},
  pages={533-552},
  year={2011},
}
David Shea Vela–Vick. ON THE TRANSVERSE INVARIANT FOR BINDINGS OF OPEN BOOKS. 2011. Vol. 88. In Journal of Differential Geometry. pp.533-552. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913205337475781893.
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