Algebraic & Geometric Topology

On Lagrangian embeddings of closed nonorientable $3$–manifolds

Toru Yoshiyasu

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We prove that for any compact orientable connected 3–manifold with torus boundary, a concatenation of it and the direct product of the circle and the Klein bottle with an open 2–disk removed admits a Lagrangian embedding into the standard symplectic 6–space. Moreover, the minimal Maslov number of the Lagrangian embedding is equal to 1.

Article information

Algebr. Geom. Topol., Volume 19, Number 4 (2019), 1619-1630.

Received: 4 November 2016
Revised: 23 December 2018
Accepted: 10 February 2019
First available in Project Euclid: 22 August 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53D12: Lagrangian submanifolds; Maslov index
Secondary: 57N35: Embeddings and immersions 57R17: Symplectic and contact topology

Lagrangian submanifold $h$–principle loose Legendrian Lagrangian cobordism Lagrangian surgery Maslov index


Yoshiyasu, Toru. On Lagrangian embeddings of closed nonorientable $3$–manifolds. Algebr. Geom. Topol. 19 (2019), no. 4, 1619--1630. doi:10.2140/agt.2019.19.1619.

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