#### Volume 19, issue 4 (2019)

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On Lagrangian embeddings of closed nonorientable $3$–manifolds

### Toru Yoshiyasu

Algebraic & Geometric Topology 19 (2019) 1619–1630
##### Abstract

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 $1$.

##### Keywords
Lagrangian submanifold, $h$–principle, loose Legendrian, Lagrangian cobordism, Lagrangian surgery, Maslov index
##### Mathematical Subject Classification 2010
Primary: 53D12
Secondary: 57N35, 57R17
##### Publication
Received: 4 November 2016
Revised: 23 December 2018
Accepted: 10 February 2019
Published: 16 August 2019
##### Authors
 Toru Yoshiyasu Center for Genomic Medicine Graduate School of Medicine Kyoto University Kyoto Japan https://sites.google.com/site/toruyoshiyasu/