On connected sums and Legendrian knots

By John B. Etnyre, K. Honda. 2003

86 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/83a67917397427749744293f3c33363368ac4a6b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. A. Stipsicz
2. Peter S. Ozsv'ath
3. P. Lisca
4. John A. Baldwin
5. Zolt'an Szab'o
6. Lenhard L. Ng
7. Tam'as K'alm'an
8. John B. Etnyre

In Geometry and Topology

1. A. Stipsicz
2. P. Lisca
3. Peter S. Ozsv'ath
4. John B. Etnyre
5. Zolt'an Szab'o
6. John A. Baldwin
7. Lenhard L. Ng
8. K. Honda

In Mathematical Physics

1. A. Stipsicz
2. P. Lisca
3. John B. Etnyre
4. John A. Baldwin
5. Peter S. Ozsv'ath
6. Zolt'an Szab'o
7. Lenhard L. Ng
8. K. Honda

Citations in the corpus

• Legendrian and Transversal Knots (2003, background): “This is a simple exercise, or see [36].”
• On the equivalence of Legendrian and transverse invariants in knot Floer homology (2011, background): “While it is known that some knot types are simple (Eliashberg and Fraser [9], and Etnyre and Honda [14; 15]), most appear not to be.”
• Legendrian ambient surgery and Legendrian contact homology (2012, background): “a new (transverse) Reeb chord 4 G. DIMITROGLOU RIZELL appearing on LS which is of degree |cS| = n−k−1. We say that LS ⊂ Y is obtained from Lby a Legendrian ambient surgery on S(see Definition 4.6). In [23] the cusp-connect sum was shown to be a well-defined operation on Legendrian knots. We establish ”
• Legendrian and transverse twist knots (2010, background): “In particular, there are knot types that are Legendrian nonsimple but transversely simple [9], whereas any transversely nonsimple knot must be Legendrian nonsimple as well.”
• Contact homology and one parameter families of Legendrian knots (2004, background): “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 ”
• Heegard Floer invariants of Legendrian knots in contact three-manifolds (2008, methodology): “We want to relate the invariants of L1 and L2 to the invariants of the connected sum L1 # L2 ⊂ (Y1 # Y2, ξ1 # ξ2) (see [14] for the definition of the connected sum operation in the contact setting).”
• Cabling and transverse simplicity (2003, background): “then L′ can be written as L′ 1#L′2 , with L′ i ∈ L(K i), i = 1,2. Each L′ i can be destabilized to a maximal tbrepresentative L′′ i by the UTP for each K i. Since tb(K 1#K 2) = tb(K 1)+tb(K 2) +1, by [EH2], we simply take L′′ = L′′ 1 #L′′2. This proves Theorem 1.4. 5. Non-uniformly-thick knots and n”
• Handle moves in contact surgery diagrams (2008, background): “3 in [14], uses the classification of tight contact structures on solid tori.”