#### Volume 15, issue 4 (2015)

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Lagrangian cobordisms via generating families: Construction and geography

### Frédéric Bourgeois, Joshua M Sabloff and Lisa Traynor

Algebraic & Geometric Topology 15 (2015) 2439–2477
##### Abstract

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 ${ℝ}^{2n+1}$ or in the $1$–jet space of any compact $n$–manifold with $n\ge 2$.

##### Keywords
Lagrangian cobordism, Legendrian submanifold, duality
##### Mathematical Subject Classification 2010
Primary: 57R17
Secondary: 53D12, 53D42