2014/09/18 by Frédéric Bourgeois, Frederic Bourgeois, Joshua M. Sabloff +2 · 2 citations
Mathematics · #Duality (order theory) #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Lagrangian #Space (punctuation) #Submanifold #math.SG #msc:53D12 #msc:53D42 #msc:57R17
paper · pdf · doi:10.2140/agt.2015.15.2439
published as Algebr. Geom. Topol. 15 (2015) 2439-2477 · 34 pages, 11 figures. v2: corrected a reference
arxiv created 2014/09/18 · openalex publication_date 2015/09/10 · arxiv updated 2015/09/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 2nC1 or in the 1-jet space of any compact n-manifold with n 2.