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 R^{2n+1} or in the 1-jet space of any compact n-manifold with n at least 2.

34 pages, 11 figures. v2: corrected a reference

References in corpus (1)

• Generating family invariants for Legendrian links of unknots

Cited by in corpus (12)

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• Cross-sections of unknotted ribbon disks and algebraic curves
• Upper bounds for the Lagrangian cobordism relation on Legendrian links
• On torsion in linearized Legendrian contact homology
• Non-Orientable Lagrangian Cobordisms between Legendrian Knots
• Geography of bilinearized Legendrian contact homology
• Weinstein presentations for high-dimensional antisurgery
• Lagrangian concordance is not a partial order in high dimensions