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arXiv · 1712.01182

The classification of Lagrangians nearby the Whitney immersion

Georgios Dimitroglou Rizell
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Abstract

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 either are 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.

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BibTeXRIS

Georgios Dimitroglou Rizell. 2019-03-27. The classification of Lagrangians nearby the Whitney immersion. https://doi.org/10.2140/gt.2019.23.3367

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