Geometric and Topological Analysis of Financial Market Structure: Evidence from Turkish Markets and the 2022–2023 Structural Break

The financial market correlation structure exhibits dynamic evolution with implications for systemic risk and diversification benefits; yet, conventional approaches using correlation magnitude monitoring may miss fundamental organizational changes. This study develops an integrated geometric–topological framework synthesizing Riemannian manifold geometry with discrete network topology to characterize market structure transformations, applying the methodology to Turkish financial markets spanning May 2015–May 2025. The analysis employs intrinsic dimensionality estimation, curvature tensor computation, and Forman–Ricci curvature calculation alongside correlation network topology measures across seventeen variables, including sectoral equity indices and macroeconomic indicators. The results document an extraordinary mid-2022 structural break featuring dimensional collapse from 2.4 to 0.43 dimensions, network density surge to 0.97, and Ricci curvature spike to 16.0, establishing a persistent hypersynchronized regime evident through 2024–2025 with density elevated by 44% and the Ricci curvature being amplified 258% above the baseline. A comparative crisis analysis reveals heterogeneous structural signatures distinguishing COVID-19 geometric vulnerability from currency crisis modular reorganization. Macro-financial linkages identify credit growth as primary structural driver, achieving r=0.504 correlation with geometric resilience. The findings demonstrate that markets undergo permanent structural transformations responding systematically to monetary–credit conditions, with implications for surveillance frameworks, stress testing design, and macroprudential policy.