Hamiltonian unknottedness of certain monotone Lagrangian tori in $S^2\times S^2$

Kai Cieliebak and Martin Schwingenheuer

Vol. 299 (2019), No. 2, 427–468

DOI: 10.2140/pjm.2019.299.427

Abstract

We prove that a monotone Lagrangian torus in $S^2\times S^2$ which suitably sits in a symplectic fibration with two sections in its complement is Hamiltonian isotopic to the Clifford torus.

Keywords

Hamiltonian isotopy, Lagrangian tori, symplectic fibrations

Mathematical Subject Classification 2010

Primary: 53D12

Secondary: 57R17

Milestones

Received: 14 May 2018

Accepted: 13 June 2018

Published: 21 May 2019