## Algebraic & Geometric Topology

### Lagrangian cobordisms via generating families: Construction and geography

#### 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 $ℝ2n+1$ 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
Accepted: 25 November 2014
First available in Project Euclid: 16 November 2017

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

#### 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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