Lagrangian Cobordisms via Generating Families: Constructions and Geography
Abstract
Embedded Lagrangian cobordisms between Legendrian submanifolds are produced from 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 non-classical 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 at least 2.
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