Lagrangian cobordisms via generating families: Construction and geography

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 $n\ge 2$.