Exact Lagrangian immersions with a single double point

Ekholm, Tobias¹ ; Smith, Ivan²

¹ Department of Mathematics, Uppsala University, Box 480, Uppsala 751 06, Sweden; and Institut Mittag-Leffler, Aurav. 17, Djursholm 182 60, Sweden
² Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, United Kingdom

Journal of the American Mathematical Society, Tome 29 (2016) no. 1, pp. 1-59

Résumé

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 $K$.

Détail

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

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