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Lagrangian cobordisms via generating families: Construction and geography

Frédéric Bourgeois, Joshua M Sabloff and Lisa Traynor

Algebraic & Geometric Topology 15 (2015) 2439–2477
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 2n+1 or in the 1–jet space of any compact n–manifold with n 2.

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Keywords
Lagrangian cobordism, Legendrian submanifold, duality
Mathematical Subject Classification 2010
Primary: 57R17
Secondary: 53D12, 53D42
References
Publication
Received: 18 September 2014
Accepted: 25 November 2014
Published: 10 September 2015
Authors
Frédéric Bourgeois
Laboratoire de Mathématiques d’Orsay
Université Paris-Sud
Bâtiment 425
F-91405 Orsay
France
http://www.math.u-psud.fr/~bourgeois/
Joshua M Sabloff
Department of Mathematics and Statistics
Haverford College
370 Lancaster Ave
Haverford, PA 19041
United States
http://www.haverford.edu/math/jsabloff/
Lisa Traynor
Department of Mathematics
Bryn Mawr College
Bryn Mawr, PA 19010
United States
http://www.brynmawr.edu/math/Math/people/traynor/intro.html