Volume 15, issue 4 (2015)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 16
Issue 4, 1827–2458
Issue 3, 1253–1825
Issue 2, 621–1251
Issue 1, 1–620

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Lagrangian cobordisms via generating families: Construction and geography

Frédéric Bourgeois, Joshua M Sabloff and Lisa Traynor

Algebraic & Geometric Topology 15 (2015) 2439–2477

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.

Lagrangian cobordism, Legendrian submanifold, duality
Mathematical Subject Classification 2010
Primary: 57R17
Secondary: 53D12, 53D42
Received: 18 September 2014
Accepted: 25 November 2014
Published: 10 September 2015
Frédéric Bourgeois
Laboratoire de Mathématiques d’Orsay
Université Paris-Sud
Bâtiment 425
F-91405 Orsay
Joshua M Sabloff
Department of Mathematics and Statistics
Haverford College
370 Lancaster Ave
Haverford, PA 19041
United States
Lisa Traynor
Department of Mathematics
Bryn Mawr College
Bryn Mawr, PA 19010
United States