Homological Lagrangian monodromy

TL;DR

This paper proves that the homological version of the Hamiltonian Lagrangian monodromy group is trivial for weakly exact Lagrangian submanifolds, using a sheaf approach to Floer homology and Seidel morphisms.

Contribution

It introduces a sheaf-based method to analyze Floer homology, establishing triviality of the homological monodromy group for weakly exact Lagrangians.

Findings

Homological Lagrangian monodromy group is trivial for weakly exact Lagrangians

Sheaf approach to Floer homology is effective in this context

Uses relative Seidel morphism to prove the result

Abstract

We show that the Hamiltonian Lagrangian monodromy group, in its homological version, is trivial for any weakly exact Lagrangian submanifold of a symplectic manifold. The proof relies on a sheaf approach to Floer homology given by a relative Seidel morphism.