## Geometry & Topology

### The classification of Lagrangians nearby the Whitney immersion

Georgios Dimitroglou Rizell

#### 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 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

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

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

https://projecteuclid.org/euclid.gt/1578366031

Digital Object Identifier
doi:10.2140/gt.2019.23.3367

Mathematical Reviews number (MathSciNet)
MR4059087

Subjects
Primary: 53D12: Lagrangian submanifolds; Maslov index

#### Citation

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. https://projecteuclid.org/euclid.gt/1578366031

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