Algebraic & Geometric Topology

Lagrangian cobordisms via generating families: Construction and geography

Frédéric Bourgeois, Joshua M Sabloff, and Lisa Traynor

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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.

Article information

Source
Algebr. Geom. Topol., Volume 15, Number 4 (2015), 2439-2477.

Dates
Received: 18 September 2014
Accepted: 25 November 2014
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841008

Digital Object Identifier
doi:10.2140/agt.2015.15.2439

Mathematical Reviews number (MathSciNet)
MR3402346

Zentralblatt MATH identifier
1330.57037

Subjects
Primary: 57R17: Symplectic and contact topology
Secondary: 53D12: Lagrangian submanifolds; Maslov index 53D42: Symplectic field theory; contact homology

Keywords
Lagrangian cobordism Legendrian submanifold duality

Citation

Bourgeois, Frédéric; Sabloff, Joshua M; Traynor, Lisa. Lagrangian cobordisms via generating families: Construction and geography. Algebr. Geom. Topol. 15 (2015), no. 4, 2439--2477. doi:10.2140/agt.2015.15.2439. https://projecteuclid.org/euclid.agt/1510841008


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