Exact Lagrangian immersions with a single double point

Ekholm, Tobias; Smith, Ivan

doi:10.1090/S0894-0347-2015-00825-6

Exact Lagrangian immersions with a single double point
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by Tobias Ekholm and Ivan Smith

J. Amer. Math. Soc. 29 (2016), 1-59

DOI: https://doi.org/10.1090/S0894-0347-2015-00825-6

Published electronically: January 9, 2015

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Abstract:

We show that if a closed orientable $2k$-manifold $K$, $k>2$, with Euler characteristic $\chi (K)\ne -2$ admits an exact Lagrangian immersion into $\mathbb {C}^{2k}$ with one transverse double point and no other self-intersections, then $K$ is diffeomorphic to the sphere. The proof combines Floer homological arguments with a detailed study of moduli spaces of holomorphic disks with boundary in a monotone Lagrangian submanifold obtained by Lagrange surgery on $K$.

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