• Corpus ID: 119581532

The Legendrian satellite construction

@article{Ng2001TheLS,
  title={The Legendrian satellite construction},
  author={Lenhard L. Ng},
  journal={arXiv: Geometric Topology},
  year={2001}
}
  • Lenhard L. Ng
  • Published 11 December 2001
  • Mathematics
  • arXiv: Geometric Topology
We examine the Legendrian analogue of the topological satellite construction for knots, and deduce some results for specific Legendrian knots and links in standard contact three-space and the solid torus. In particular, we show that the Chekanov-Eliashberg contact homology invariants of Legendrian Whitehead doubles of stabilized knots contain no nonclassical information. 
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References

SHOWING 1-3 OF 3 REFERENCES
Generating function polynomials for legendrian links
It is shown that, in the 1{jet space of the circle, the swapping and the flyping procedures, which produce topologically equivalent links, can produce nonequivalent legendrian links. Each component
Differential algebra of Legendrian links
Let the space R = {(q, p, u)} be equipped with the standard contact form α = du − pdq. A link L ⊂ R3 is called Legendrian if the restriction of α to L vanishes. Two Legendrian links are said to be