Background: Brain tumor segmentation requires precise delineation of hierarchical structures from multi-sequence MRI. However, existing deep learning methods primarily rely on visual features, showing insufficient discriminative power in ambiguous boundary regions. Moreover, they lack explicit integration of medical domain knowledge such as anatomical semantics and geometric topology. Methods: We propose a knowledge-guided framework, Synchronized Tri-modal Prior Fusion (STPF), that explicitly integrates three heterogeneous knowledge priors: pathology-driven differential features (T1ce-T1, T2-FLAIR, T1/T2) encoding contrast patterns; unsupervised semantic descriptions transformed into voxel-level guidance via spatialization operators; and geometric constraints extracted through persistent homology analysis. A dual-level fusion architecture dynamically allocates prior weights at the voxel level based on confidence and at the sample level through hypernetwork-generated conditional vectors. Furthermore, nested output heads structurally ensure the hierarchical constraint ET subset TC subset WT. Results: STPF achieves a mean Dice coefficient of 0.868 on the BraTS 2020 dataset, surpassing the best baseline by 2.6 percentage points (3.09% relative improvement). Notably, five-fold cross-validation yields coefficients of variation between 0.23% and 0.33%, demonstrating stable performance. Additionally, ablation experiments show that removing topological and semantic priors leads to performance degradation of 2.8% and 3.5%, respectively. Conclusions: By explicitly integrating medical knowledge priors - anatomical semantics and geometric constraints - STPF improves segmentation accuracy in ambiguous boundary regions while demonstrating generalization capability and clinical deployment potential.