Lagrangian cobordisms via generating families: Construction and geography
Author Full Names:
Bourgeois, Frederic; Sabloff, Joshua M.; Traynor, Lisa
ALGEBRAIC AND GEOMETRIC TOPOLOGY, 15 (4):2439-2477; 10.2140/agt.2015.15.2439 2015
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.