The classification of Lagrangians nearby the Whitney immersion

Dimitroglou Rizell, Georgios¹

¹ Department of Mathematics, Uppsala University, Uppsala, Sweden

Geometry & topology, Tome 23 (2019) no. 7, pp. 3367-3458.

Résumé

The Whitney immersion is a Lagrangian sphere inside the four-dimensional symplectic vector space which has a single transverse double point of Whitney self-intersection number $+1$. This Lagrangian also arises as the Weinstein skeleton of the complement of a binodal cubic curve inside the projective plane, and the latter Weinstein manifold is thus the “standard” neighbourhood of Lagrangian immersions of this type. We classify the Lagrangians inside such a neighbourhood which are homologically essential, and which are either embedded or immersed with a single double point; they are shown to be Hamiltonian isotopic to either product tori, Chekanov tori, or rescalings of the Whitney immersion.

Détail

DOI : 10.2140/gt.2019.23.3367

Classification : 53D12
Keywords: nearby Lagrangian conjecture, Lagrangian fibration, Clifford torus, Chekanov torus, Whitney immersion, Whitney sphere

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