Homological Lagrangian monodromy for some monotone tori

2022/01/25 by Augustynowicz, Marcin, Smith, Jack, Wornbard, Jakub
#53D12 #53D40 #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2201.10507

Abstract

Given a Lagrangian submanifold L in a symplectic manifold X, the homological Lagrangian monodromy group H_L describes how Hamiltonian diffeomorphisms of X preserving L setwise act on H_*(L). We begin a systematic study of this group when L is a monotone Lagrangian n-torus. Among other things, we describe H_L completely when L is a monotone toric fibre, make significant progress towards classifying the groups than can occur for n=2, and make a conjecture for general n. Our classification results rely crucially on arithmetic properties of Floer cohomology rings.

Related

• Monodromy groups of Lagrangian tori in the symplectic 4-space
• Monodromy and isotopy of monotone Lagrangian tori
• Homological Lagrangian monodromy and Wang exact sequence
• C⁰ Lagrangian Monodromy
• Notes on monotone Lagrangian twist tori