Papers › Homological Lagrangian monodromy for some monotone tori
Homological Lagrangian monodromy for some monotone tori
Marcin Augustynowicz, Jack Smith, Jakub Wornbard
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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.
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