On linking of Lagrangian tori in ℝ⁴

2018/06/20 by Côté, Laurent
#FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1806.07853

Abstract

We prove some results about linking of Lagrangian tori in the symplectic vector space (ℝ⁴, ω). 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 ℝ⁴ and also strengthen their conclusions in the monotone case in ℝ⁴.

Related

• Linking of Lagrangian Tori and Embedding Obstructions in Symplectic 4-Manifolds
• Semi-Local Exotic Lagrangian Tori in Dimension Four
• Tori in symplectic 4-manifolds
• Notes on monotone Lagrangian twist tori
• Monodromy groups of Lagrangian tori in the symplectic 4-space