Lagrangian cobordisms via generating families: Construction and geography

Frédéric Bourgeois, Joshua M Sabloff, Lisa Traynor
2015 Algebraic and Geometric Topology  
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
more » ... mily 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.
doi:10.2140/agt.2015.15.2439 fatcat:uzxpumsvpbg77nnjvqsk5lxfxu