Geometry & Topology

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

Permanent link to this document
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

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

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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