The classification of Lagrangians nearby the Whitney immersion

Dimitroglou Rizell, Georgios

doi:10.2140/gt.2019.23.3367

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The classification of Lagrangians nearby the Whitney immersion

Georgios Dimitroglou Rizell

Geometry & Topology 23 (2019) 3367–3458

DOI: 10.2140/gt.2019.23.3367

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.

Keywords

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

Mathematical Subject Classification 2010

Primary: 53D12

References

Publication

Received: 5 March 2018

Revised: 23 October 2018

Accepted: 7 March 2019

Published: 30 December 2019

Proposed: Yasha Eliashberg

Seconded: Ciprian Manolescu, Leonid Polterovich

Authors

Georgios Dimitroglou Rizell
Department of Mathematics Uppsala University Uppsala Sweden

Volume 23, issue 7 (2019)