Geometry & Topology

The classification of Lagrangians nearby the Whitney immersion

Georgios Dimitroglou Rizell

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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.

Article information

Geom. Topol., Volume 23, Number 7 (2019), 3367-3458.

Received: 5 March 2018
Revised: 23 October 2018
Accepted: 7 March 2019
First available in Project Euclid: 7 January 2020

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Primary: 53D12: Lagrangian submanifolds; Maslov index

nearby Lagrangian conjecture Lagrangian fibration Clifford torus Chekanov torus Whitney immersion Whitney sphere


Dimitroglou Rizell, Georgios. The classification of Lagrangians nearby the Whitney immersion. Geom. Topol. 23 (2019), no. 7, 3367--3458. doi:10.2140/gt.2019.23.3367.

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