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Lagrangian cobordisms
via generating families: Construction and geography
Frédéric Bourgeois, Joshua M Sabloff and Lisa Traynor |
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Algebraic & Geometric Topology 15 (2015) 2439–2477
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Abstract |
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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 or in the –jet space of any compact –manifold with . Corrections were submitted on 7 Oct 2023 and posted online on 15 Oct 2023. |
Keywords
Lagrangian cobordism, Legendrian submanifold, duality
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Mathematical Subject Classification 2010
Primary: 57R17
Secondary: 53D12, 53D42
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Supplementary material |
References |
Publication
Received: 18 September 2014
Accepted: 25 November 2014
Published: 10 September 2015
Correction: 15 October 2023 |
Authors |
| Frédéric Bourgeois | |
| Laboratoire de Mathématiques
d’Orsay Université Paris-Sud Bâtiment 425 F-91405 Orsay France |
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| 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 |
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| http://www.haverford.edu/math/jsabloff/ | |
| Lisa Traynor | |
| Department of Mathematics Bryn Mawr College Bryn Mawr, PA 19010 United States |
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| http://www.brynmawr.edu/math/Math/people/traynor/intro.html | |
| © 2015 MSP (Mathematical Sciences Publishers). |
