Volume 15, issue 4 (2015)

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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 ${ℝ}^{2n+1}$ or in the $1$–jet space of any compact $n$–manifold with $n\ge 2$.

Keywords
Lagrangian cobordism, Legendrian submanifold, duality
Mathematical Subject Classification 2010
Primary: 57R17
Secondary: 53D12, 53D42
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