Knots and Contact Geometry I: Torus Knots and the Figure Eight Knot
By John B. Etnyre, K. Honda. 2001
240 citations recorded by the source corpus.
Subfields: Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/e0f5b302b37bf4c5e85fae01c27341b5cf0b87af
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
- A. Stipsicz
- Lenhard L. Ng
- John B. Etnyre
- Peter S. Ozsv'ath
- P. Lisca
- Zolt'an Szab'o
- Michael C. Sullivan
- T. Ekholm
Citations in the corpus
- Cabling, contact structures and mapping class monoids (2010, background): “Thus K and K ′ have the same transverse push-offs, see [18].”
- Rational linking and contact geometry (2009, methodology): “To finish the classification of Legendrian knots in the knot type of K1 we need to identify the rational rotation number of the Legendrian knot L in the knot type of K1 with maximal rational Thurston-Bennequin invariant.”
- Infinitely many Lagrangian fillings (2020, background): “Positive Legendrian torus knots are Legendrian simple positive braids [23], and thus are uniquely determined by their ThurstonBennequin invariants and their rotation numbers.”
- Legendrian and Transversal Knots (2003, background): “Theorem 5.8 (Etnyre and Honda 2001, [37]).”
- Heegard Floer invariants of Legendrian knots in contact three-manifolds (2008, background): “Transverse knots admit a preferred orientation, and can be approximated, uniquely up to negative stabilization, by oriented Legendrian knots [9, 13].”
- Invariants of Legendrian Knots (2003, background): “Their proof uses the classification of Legendrian torus knots given in [8].”
- Contact homology and one parameter families of Legendrian knots (2004, methodology): “AMS Classification numbers Primary: 53D40 Secondary: 57M25 Keywords: Legendrian contact homology, monodromy, Reidemeister moves, braid positive knots, torus knots Proposed: Yasha Eliashberg Received: 3 October 2004 Seconded: Peter Ozsváth, Tomasz Mrowka Revised: 24 July 2005 c© Geometry & Topology…”
- Non-isotopic Legendrian submanifolds in R2n+1 (2005, unknown): “85”
- Topologically Trivial Legendrian Knots (2008, background): “Honda in [EtHo1] classified Legendrian torus knots and figure-eight knots.”