A method for characterizing the topological fluctuations in liquids is proposed. This approach exploits the concept of the weighted gyration tensor of a collection of particles and permits the definition of a local configurational unit (LCU). The first principal axis of the gyration tensor serves as the director of the LCU, which can be tracked and analyzed by molecular dynamics simulations. Analysis of moderately supercooled Kob–Andersen mixtures suggests that orientational relaxation of the LCU closely follows viscoelastic relaxation and exhibits a two-stage behavior. The slow relaxing component of the LCU corresponds to the structural, Maxwellian mechanical relaxation. Additionally, it is found that the mean curvature of the LCUs is approximately zero at the Maxwell relaxation time with the Gaussian curvature being negative. This observation implies that structural relaxation occurs when the configurationally stable and destabilized regions interpenetrate each other in a bicontinuous manner. Finally, the mean and Gaussian curvatures of the LCUs can serve as reduced variables for the shear stress correlation, providing a compelling proof of the close connection between viscoelastic relaxation and topological fluctuations in glass-forming liquids.
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