Geodesic
Lagrangian cobordisms via generating families: Construction and geography
Bourgeois, Frédéric1 ; Sabloff, Joshua M2 ; Traynor, Lisa3
1 Laboratoire de Mathématiques d’Orsay, Université Paris-Sud, Bâtiment 425, F-91405 Orsay, France
2 Department of Mathematics and Statistics, Haverford College, 370 Lancaster Ave, Haverford, PA 19041, United States
3 Department of Mathematics, Bryn Mawr College, Bryn Mawr, PA 19010, United States
Algebraic and Geometric Topology, Tome 15 (2015) no. 4, pp. 2439-2477

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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 ℝ2n+1 or in the 1–jet space of any compact n–manifold with n ≥ 2.

Corrections were submitted on 7 Oct 2023 and posted online on 15 Oct 2023.

DOI : 10.2140/agt.2015.15.2439
Classification : 57R17, 53D12, 53D42
Keywords: Lagrangian cobordism, Legendrian submanifold, duality

Bourgeois, Frédéric 1 ; Sabloff, Joshua M 2 ; Traynor, Lisa 3

1 Laboratoire de Mathématiques d’Orsay, Université Paris-Sud, Bâtiment 425, F-91405 Orsay, France
2 Department of Mathematics and Statistics, Haverford College, 370 Lancaster Ave, Haverford, PA 19041, United States
3 Department of Mathematics, Bryn Mawr College, Bryn Mawr, PA 19010, United States 
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Bourgeois, Frédéric; Sabloff, Joshua M; Traynor, Lisa. Lagrangian cobordisms via generating families: Construction and geography. Algebraic and Geometric Topology, Tome 15 (2015) no. 4, pp. 2439-2477. doi: 10.2140/agt.2015.15.2439

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