Markov theorem for transversal links

By S. Orevkov, V. Shevchishin. 2001

70 citations recorded by the source corpus.

It is shown that two braids represent transversally isotopic links if and only if one can pass from one braid to another by conjugations in braid groups, positive Markov moves, and their inverses.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9e62c0a1eb7687221bb69de20bd9a0df05b6c859

How researchers see this paper

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In Geometry and Topology

1. John A. Baldwin
2. John B. Etnyre
3. J. Birman
4. William W. Menasco
5. Peter S. Ozsv'ath
6. A. Stipsicz
7. O. Plamenevskaya
8. Lenhard L. Ng

In Mathematical Physics

1. John A. Baldwin
2. John B. Etnyre
3. J. Birman
4. A. Stipsicz
5. Peter S. Ozsv'ath
6. O. Plamenevskaya
7. P. Lisca
8. Lenhard L. Ng

Citations in the corpus

• Legendrian and Transversal Knots (2003, background): “One just needs the check that the “braiding process” can be done in a transverse way. For details see [6, 76 ].”
• Stabilization in the braid groups II: Transversal simplicity of knots (2003, background): “The existence of Markov towers in the transversal setting was proved by Orevkov and Shevchisin in [15].”
• On the spectral sequence from Khovanov homology to Heegaard Floer homology (2008, background): “Conversely, it is clear that a closed braid around thez-axis may be isotoped through closed braids so that it becomes transverse (the contact planes are nearly vertical far enough from the z-axis). Theorem 5.1 ([ 10 , 20]).”