Lagrangian cobordisms via generating families: Construction and geography
By Frederick J. Bourgeois III, J. Sabloff, L. Traynor. 2014
73 citations recorded by the source corpus.
Embedded Lagrangian cobordisms between Legendrian submanifolds are produced by isotopy, spinning, and handle-attachment constructions that employ the technique of generating families. Moreover, any Legendrian with a generating family has an immersed Lagrangian filling with a compatible generating family. These constructions are applied in several directions, in particular to a nonclassical geography question: any graded group satisfying a duality condition can be realized as the generating family homology of a connected Legendrian submanifold in R 2nC1 or in the 1‐jet
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/175d995eede607755112d9d40a22edb14b2e80b5
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In Applied Mathematics
In Geometry and Topology
- Steven Sivek
- Roger Casals
- Christopher Cornwell
- Honghao Gao
- Lenhard L. Ng
- Emmy Murphy
- John B. Etnyre
- T. Ekholm
In Mathematical Physics
- Steven Sivek
- Roger Casals
- Christopher Cornwell
- Honghao Gao
- Lenhard L. Ng
- Emmy Murphy
- John B. Etnyre
- T. Ekholm
Citations in the corpus
- Infinitely many Lagrangian fillings (2020, methodology): “he rightmost cusp for the (i+1)th strand. This is depicted in the second and fth diagrams of Figure 12 in the cases of ˙ 1 and ˙ 2. Once these two cusps are aligned, we perform a reverse pinched-move [8, 47] allowing this pair of opposite cusps to become two parallel strands. This corresponds to a L”
- Obstructions to Lagrangian concordance (2014, background): “In symplectic and contact topology, there has been a great deal of recent interest in the subject of Lagrangian cobordisms between Legendrian submanifolds; see for example [1, 3, 5, 6, 8, 9, 13, 14, 26, 27, 44].”
- Legendrian fronts for affine varieties (2016, background): “The above definition might be elaborate to read, but the geometric idea is simple: it is the Legendrian analogue of a smooth surgery where vertical tangencies are substituted by cusp edges; see Figure 15 for an example and the discussions in [13] for more details.”