The Markov Theorem for transverse knots
By Nancy C. Wrinkle. 2002
59 citations recorded by the source corpus.
A transverse knot is a knot that is transverse to the planes of the standard contact structure on real 3-space. In this paper we prove the Markov Theorem for transverse braids, 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 paper (BM02), modified to the transverse setting. The modification is straightforward until we get to the special case of preferred longitudes, where we need some new machinery. We use techniques from earlier work by the author with Birman (BW00), by Birman and Menasco ((BM4), for example), and develop new methods from Cromwell's paper on arc-presentations (Cr95).
Subfields: Artificial Intelligence, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/8d3166c4e68231263a443308fecd370a7b2edbe4
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Citations in the corpus
- On the spectral sequence from Khovanov homology to Heegaard Floer homology (2008, background): “This spectral sequence behaves nicely under connected sums.”
- Markov theorem for transversal links (2001, unknown): “Another proof of the theorem based on completely different ideas was independently obtained by Nancy Wrinkle in her PhD thesis [ 14 ].”
- Legendrian and Transversal Knots (2003, unknown): “11 (Orevkov and Shevchishin 2003, [76]; Wrinkle, [86]).”
- On the equivalence of Legendrian and transverse invariants in knot Floer homology (2011, background): “In addition, Pavelescu proves the following generalization of Wrinkle’s Transverse Markov Theorem [42] (see also Orevkov and Shevchishin [28]).”