Reconstructing dynamic scenes and objects from monocular egocentric video is crucial for embodied AI, yet existing 4D Gaussian Splatting (4DGS) approaches struggle with everyday interactions involving topological changes, such as cutting, assembly, opening, or closing. Since 4DGS methods rely on deforming a fixed representation, events that split, merge, or reveal surfaces cause severe visual artifacts. To address this challenge, we introduce TopoEgo, the first benchmark dedicated to topological changes in egocentric video (covering fission, fusion, open, and close), alongside Topo-4DGS, a topology-aware reconstruction method. Topo4DGS jointly models part-level motion and time-varying surface support by assigning independent rigid transformations to interacting parts and dynamically activating or deactivating Gaussians as surfaces appear, disappear, or separate. Extensive experiments demonstrate that Topo-4DGS significantly outperforms state-of-the-art 4DGS approaches across topological changes, especially on post-event frames. Code and data will be made publicly available.

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