The Markov Theorem for Transverse Knots

@inproceedings{Wrinkle2002TheMT,
  title={The Markov Theorem for Transverse Knots},
  author={Nancy C Wrinkle},
  year={2002}
}
  • Nancy C Wrinkle
  • Published 2002
Let ξ be the standard contact structure in oriented IR 3 = (ρ, θ, z) given as the kernel of the 1-form α = ρ 2 dθ + dz. A transverse knot is a knot that is transverse to the planes of this contact structure. In this paper we prove the Markov Theorem for transverse knots, which states that two transverse closed braids that are isotopic as transverse knots are also isotopic as transverse braids. The methods of the proof are based on Birman and Menasco's proof of the Markov Theorem in their recent… CONTINUE READING
Highly Cited
This paper has 21 citations. REVIEW CITATIONS

References

Publications referenced by this paper.
Showing 1-9 of 9 references

Invariants of Legendrian and transverse knots in the standard contact space

  • D Fuchs, S Tabachnikov
  • Topology
  • 1997

Embedding knots and links in an open book II: Bounds on arc index

  • P R Cromwell, I J Nutt
  • Math. Proc. Camb. Phil. Soc
  • 1996

Embedding knots and links in an open book I: Basic properties

  • P R Cromwell
  • Topology and its Applications
  • 1995

Special positions for essential tori in link complements, Topology

  • J S Birman, W Menasco
  • Special positions for essential tori in link…
  • 1994

On the isotopy of Legendrian knots

  • J Swiatkowski
  • Ann. Glob. Anal. Geom
  • 1992

English version: Russian Math

  • D Bennequin, Entrelacements De, Pfaff
  • English version: Russian Math
  • 1983

On Markov's Theorem, Proceedings KNOTS-2000

  • J S Birman, W W Menasco
  • On Markov's Theorem, Proceedings KNOTS-2000

Similar Papers

Loading similar papers…