On Lagrangian embeddings of closed nonorientable 3–manifolds

Yoshiyasu, Toru

doi:10.2140/agt.2019.19.1619

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On Lagrangian embeddings of closed nonorientable $3$–manifolds

Toru Yoshiyasu

Algebraic & Geometric Topology 19 (2019) 1619–1630

DOI: 10.2140/agt.2019.19.1619

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

References

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/

Volume 19, issue 4 (2019)