This study explores the topological characterization of rearrangements in amorphous solids, focusing on shear transformations (STs) and their role in plasticity. The authors apply topological defect concepts from liquid crystals to analyze vibrational eigenmodes, relating these defects to displacement fields characterized by orientation and magnitude of eigenstrain. They demonstrate that these parameters can be used to characterize plastic stress relaxation and estimate stress drops accurately. The study uses 2D binary Lennard-Jones glass squares to simulate simple shear deformation, identifying STs through topological defects in the displacement field. The orientation and magnitude of these defects are then used to fit the Eshelby inclusion model, which accurately reproduces the displacement field and stress relaxation. The results confirm the localized nature of displacements controlling long-range deformation and stress relaxation, highlighting the importance of topological defects in understanding amorphous material behavior.This study explores the topological characterization of rearrangements in amorphous solids, focusing on shear transformations (STs) and their role in plasticity. The authors apply topological defect concepts from liquid crystals to analyze vibrational eigenmodes, relating these defects to displacement fields characterized by orientation and magnitude of eigenstrain. They demonstrate that these parameters can be used to characterize plastic stress relaxation and estimate stress drops accurately. The study uses 2D binary Lennard-Jones glass squares to simulate simple shear deformation, identifying STs through topological defects in the displacement field. The orientation and magnitude of these defects are then used to fit the Eshelby inclusion model, which accurately reproduces the displacement field and stress relaxation. The results confirm the localized nature of displacements controlling long-range deformation and stress relaxation, highlighting the importance of topological defects in understanding amorphous material behavior.