Stabilization in the braid groups II: Transversal simplicity of knots
By J. Birman, William W. Menasco. 2003
74 citations recorded by the source corpus.
The main result of this paper is a negative answer to the question: are all transversal knot types transversally simple? An explicit infinite family of examples is given of closed 3-braids that define transversal knot types that are not transversally simple. The method of proof is topological and indirect.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3c26e84987f591ad50c8e3c0a51ec9885eced75e
How researchers see this paper
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In Geometry and Topology
- A. Stipsicz
- Lenhard L. Ng
- Peter S. Ozsv'ath
- John B. Etnyre
- Zolt'an Szab'o
- Dylan Thurston
- O. Plamenevskaya
- M. Hedden
In Mathematical Physics
- A. Stipsicz
- Lenhard L. Ng
- Peter S. Ozsv'ath
- John B. Etnyre
- Zolt'an Szab'o
- Dylan Thurston
- O. Plamenevskaya
- John A. Baldwin
Citations in the corpus
- Transverse knots distinguished by knot Floer homology (2007, methodology): “We have not yet investigated the precise dependence of b �M on the sequence of moves M (though see Section 5), and this may be the input required to distinguish the three-braid examples of Birman and Menasco [ 3 ].”
- Essential open book foliations and fractional Dehn twist coefficient (2012, background): “on F. If it satisfies certain conditions we call it open book foliation and denote it by Fob(F). The open book foliation has its origin in Bennequin’s work [1] and Birman and Menasco’s braid foliation [3, 4, 5, 6, 7, 8, 9, 10, 11], where the underlying manifold M∼= S3. Let us recall Giroux’s seminal ”
- Contact surgeries and the transverse invariant in knot Floer homology (2008, methodology): “not typeis said to betransversely simple if it hasno such pairs of transverse representatives. The first examples of transversely non–simple knot types were found by EtnyreHonda [7] and Birman-Menasco [3], and further examples were found in [15]. We will use Theorem 1.1 to show the following: 2 Theor”
- Transverse knots and Khovanov homology (2004, methodology): “However, the existing examples are sparse (those of [EH3] are not even explicit), and the proofs in [ BM ] and [EH3] require a subtle analysis of specific braids and contact manifolds.”
- Legendrian and Transversal Knots (2003, background): “Many other examples arise from Birman and Menasco’s analysis, see [8, 9], but they are all three braids.”