This study investigates the topological characterization of rearrangements in amorphous solids, focusing on how plasticity is localized and occurs as shear transformations. The research applies topological defect concepts from liquid crystals to analyze vibrational eigenmodes, identifying -1 topological defects linked to Eshelby inclusions. These defects are characterized by orientation and magnitude, which are used to predict plastic stress relaxation and local structural rearrangements. The study confirms that these defects are essential for understanding the localized nature of displacements that control both long-range deformation and stress relaxation. In amorphous materials, the absence of a lattice structure makes it challenging to define discrete defects. However, the study shows that structural defects can be identified through non-affine displacements and high potential energy release. These shear transformations (STs) are irreversible atomic displacements that contribute to the transition between inherent structures. STs are quantified by number and activation energy and are integrated into constitutive equations for modeling plasticity. The study uses 2D binary Lennard-Jones glass squares to simulate and analyze plastic events. The displacement field is analyzed to identify STs, with topological defects characterized by orientation and magnitude. The results show that the displacement field can be described as a superposition of quadrupoles and vortices. The study also demonstrates that the orientation and magnitude of STs can be related to stress drops using values from either the global displacement field or the local displacement around the STs. The analysis reveals that the stress drop associated with plastic events can be accurately estimated using the position and characteristics of Eshelby inclusions. The study shows that the Eshelby inclusion model can reproduce the displacement field, with parameters fitted to the global or local displacement field. The results indicate a strong correlation between the fitted parameters and MD-measured stress drops, confirming the localized nature of displacements. The study also discusses the implications of periodic boundary conditions and size effects, showing that the model does not account for interactions between inclusions and self-interaction through the boundary conditions. However, the results suggest that the underestimation of stress relaxation is not due to these interactions. The study concludes that the rearrangements in amorphous materials are composed of discrete, local STs that can be enumerated and characterized. The topological defect concept provides an unambiguous methodology for locating and characterizing such STs in various types of glasses, including metallic and 2D systems.This study investigates the topological characterization of rearrangements in amorphous solids, focusing on how plasticity is localized and occurs as shear transformations. The research applies topological defect concepts from liquid crystals to analyze vibrational eigenmodes, identifying -1 topological defects linked to Eshelby inclusions. These defects are characterized by orientation and magnitude, which are used to predict plastic stress relaxation and local structural rearrangements. The study confirms that these defects are essential for understanding the localized nature of displacements that control both long-range deformation and stress relaxation. In amorphous materials, the absence of a lattice structure makes it challenging to define discrete defects. However, the study shows that structural defects can be identified through non-affine displacements and high potential energy release. These shear transformations (STs) are irreversible atomic displacements that contribute to the transition between inherent structures. STs are quantified by number and activation energy and are integrated into constitutive equations for modeling plasticity. The study uses 2D binary Lennard-Jones glass squares to simulate and analyze plastic events. The displacement field is analyzed to identify STs, with topological defects characterized by orientation and magnitude. The results show that the displacement field can be described as a superposition of quadrupoles and vortices. The study also demonstrates that the orientation and magnitude of STs can be related to stress drops using values from either the global displacement field or the local displacement around the STs. The analysis reveals that the stress drop associated with plastic events can be accurately estimated using the position and characteristics of Eshelby inclusions. The study shows that the Eshelby inclusion model can reproduce the displacement field, with parameters fitted to the global or local displacement field. The results indicate a strong correlation between the fitted parameters and MD-measured stress drops, confirming the localized nature of displacements. The study also discusses the implications of periodic boundary conditions and size effects, showing that the model does not account for interactions between inclusions and self-interaction through the boundary conditions. However, the results suggest that the underestimation of stress relaxation is not due to these interactions. The study concludes that the rearrangements in amorphous materials are composed of discrete, local STs that can be enumerated and characterized. The topological defect concept provides an unambiguous methodology for locating and characterizing such STs in various types of glasses, including metallic and 2D systems.