Non-isotopic Legendrian submanifolds in R2n+1

By T. Ekholm, John B. Etnyre, Michael C. Sullivan. 2005

138 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ab46857ccfdc313513c1a32d6cf331120e197a74

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In Applied Mathematics

1. T. Ekholm
2. John B. Etnyre
3. Michael C. Sullivan
4. Lenhard L. Ng
5. Frederick J. Bourgeois III
6. Georgios Dimitroglou Rizell
7. Y. Eliashberg
8. J. Sabloff

In Geometry and Topology

1. T. Ekholm
2. John B. Etnyre
3. Lenhard L. Ng
4. Michael C. Sullivan
5. Y. Eliashberg
6. Georgios Dimitroglou Rizell
7. Frederick J. Bourgeois III
8. J. Sabloff

In Mathematical Physics

1. T. Ekholm
2. John B. Etnyre
3. Michael C. Sullivan
4. Lenhard L. Ng
5. Georgios Dimitroglou Rizell
6. Y. Eliashberg
7. J. Sabloff
8. Frederick J. Bourgeois III

Citations in the corpus

• Framed knot contact homology (2004, background): “manuscript, along with its predecessors [15, 16], comprises one of the first instances of a reasonably nontrivial and involved computation of Legendrian contact homology in higher dimensions; see also [5]. (This statement tacitly assumes the pending result, mentioned above, that the combinatorial ver”
• Legendrian Contact Homology in P X R (2005, methodology): “Using the examples of non-Legendrian isotopic Legendrian submanifolds of R 2 n +1 (with its standard contact structure) constructed in [6, 8] we have the following immediate corollary.”
• Morse flow trees and Legendrian contact homology in 1-jet spaces (2005, unknown): “ar X iv :m at h/ 05 09 38 6v 1 [ m at h. SG ] 1 6 Se p 20”
• Rational symplectic field theory over Z2 for exact Lagrangian cobordisms (2006, background): “In Subsection 2.3, the vector space of an exact cobordism is defined and gluings of formal disks are interpreted as operations on such vector spaces.”
• The contact homology of Legendrian submanifolds in R2n+1 (2005, background): “In Section 5, the (formal) dimension of the moduli space of punctured holomorphic disks with boundary on an exact Lagrangian immersion which is an instant in a generic 1-parameter family is expressed in terms of its boundary data.”
• Legendrian ambient surgery and Legendrian contact homology (2012, background): “m is a well-defined operation on Legendrian knots. Since Legendrian ambient 0-surgery is a generalisation of cusp connected sum, the below proposition provides a positive answer to a question posed in [EES2]. For simplicity we here only consider the case when (Cn×R,dz− P i yidxi) is the standard cont”
• Legendrian contact homology in $P \times \mathbb{R}$ (2007, methodology): “See [6] for a review of stable tame isomorphisms.”
• Lagrangian cobordisms via generating families: Construction and geography (2014, methodology): “ rotation number vanishes; see the discussion in [9, Section 2.2], for example. Further, for even-dimensional Legendrians, the Thurston-Bennequin number is determined by the Euler characteristic; see [17] or [34, Appendix A], for example. Thus, the only interesting question for classical llable geog”
• Knot contact homology (2011, methodology): “[17] for 1-dimensional Legendrian knots in R3 with the standard contact structure. Also, computations of Legendrian homology in higher dimensions have been carried out in some circumstances; see e.g. [6, 12, 16]. The results of the present paper constitute one of the first complete and reasonably inv”
• Effect of Legendrian surgery (2009, background): “ion values of 0- jets. instead of e for the empty word of Reeb chords in this case. The Legendrian unknot ΛU ⊂R2n−1 = J1(Rn−1) is depicted in Figure 8. It has one Reeb chord a with grading |a|−1, see [19]. Using an adapted almost complex structure J0 on J1(Rn−1) ×R = T∗Rn−1 ×C induced from the stand”