Title: The classification of Lagrangians nearby the Whitney immersion,
Abstract: The Whitney immersion is a Lagrangian sphere inside the four-dimensional
symplectic vector space which has a single transverse double point of
self-intersection index $+1.$ 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 homologous to the Whitney immersion, 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.