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The dominant paradigm in cybersecurity continues to privilege infrastructure, protocol integrity, and endpoint resilience, while an increasing fraction of high-impact attacks bypasses these controls by directly manipulating human cognition. This work formalizes such attacks as structured distortions within human digital trust interactions, introducing Cognitive Topological Cybersecurity (CTC) as a rigorous analytical framework. Within this paradigm, interactions are modeled as a high-dimensional manifold whose geometry encodes trust relationships across users, communication channels, and psychological signals. The proposed Cognitive Attack Topology (CAT) framework operationalizes this view through the construction of a Trust Topology Tensor (TTT), enabling the quantification of adversarial influence via Cognitive Distortion Energy (CDE) and its normalized form, the Trust Distortion Index (TDI). A complementary Cognitive Manipulation Score (CMS) captures the composite effect of urgency, fear, authority, and persuasion signals. The framework is instantiated in a multi-layer architecture that integrates transformer- based signal decomposition with dynamic graph modeling and topological anomaly detection. Empirical evaluation is conducted on the GCT-100K dataset, a large-scale benchmark comprising real, public, and synthetically generated cognitive attack interactions. The CAT model achieves a ROC-AUC of 0.9555, exceeding conventional text-based baselines, while maintaining robustness under adversarial cloaking conditions. Notably, performance remains invariant across linguistic boundaries, with a multilingual AUC of 0.984, indicating that topological features of trust manipulation exhibit language-agnostic structure. These results establish that human-targeted cyber-attacks can be detected not as isolated semantic artifacts, but as measurable geometric perturbations in trust space, motivating a shift toward cognition-aware, topology-driven defensive systems.