Topology-consistent dynamic model sequences are essential for applications such as animation and model editing. However, existing 4D reconstruction methods face challenges in generating high-quality topology-consistent meshes. To address this, we propose a topology-aware dynamic reconstruction framework based on Gaussian Splatting. We introduce a Gaussian topological structure that explicitly encodes spatial connectivity. This structure enables topology-aware densification and pruning, preserving the manifold consistency of the Gaussian representation. Temporal regularization terms further ensure topological coherence over time, while differentiable mesh rasterization improves mesh quality. Experimental results demonstrate that our method reconstructs topology-consistent mesh sequences with significantly higher accuracy than existing approaches. Moreover, the resulting meshes enable precise 3D keypoint tracking. Project page: https://haza628.github.io/tagSplat/