Lagrangian Cobordisms via Generating Families: Constructions and Geography
Symplectic Geometry
2015-09-30 v2
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.
Keywords
Cite
@article{arxiv.1409.3152,
title = {Lagrangian Cobordisms via Generating Families: Constructions and Geography},
author = {Frederic Bourgeois and Joshua M. Sabloff and Lisa Traynor},
journal= {arXiv preprint arXiv:1409.3152},
year = {2015}
}
Comments
34 pages, 11 figures. v2: corrected a reference