Journal of Symplectic Geometry

Volume 18 (2020)

Number 2

On linking of Lagrangian tori in $\mathbb{R}^4$

Pages: 409 – 462



Laurent Côté (Department of Mathematics, Stanford University, Stanford, California, U.S.A.)


We prove some results about linking of Lagrangian tori in the symplectic vector space $(\mathbb{R}^4 , \omega)$. We show that certain enumerative counts of holomophic disks give useful information about linking. This enables us to prove, for example, that any two Clifford tori are unlinked in a strong sense. We extend work of Dimitroglou Rizell and Evans on linking of monotone Lagrangian tori to a class of non-monotone tori in $\mathbb{R}^4$ and also strengthen their conclusions in the monotone case in $\mathbb{R}^4$.

Received 13 July 2018

Accepted 30 April 2019

Published 8 June 2020