Topological Data Analysis (TDA) has gained considerable attention as a robust tool for unraveling intricate data across diverse application domains. Central to TDA is the utilization of persistent homology, a method aimed at extracting and analyzing low-dimensional topological features from high-dimensional datasets. Recently, TDA has found novel application in financial research, where the viability of its application to stock market data analysis is underscored through quantitative analysis. The analysis of stock market crashes constitutes a pivotal topic within contemporary stock market research. However, due to the volatility of stock data and the interference of noise, the detection and prediction of such crashes often pose challenges. This paper endeavors to employ the persistent homology methodology to distill topological features from the data of China’s Shanghai Stock Exchange 50 (SSE 50) stocks, including persistent diagram, persistent landscape, \(L^2\) -norm and persistent entropy. By merging statistical and machine learning methodologies, rigorous quantitative analysis is conducted. Empirical findings consistently demonstrate a high classification accuracy in distinguishing stock market crashes from normal periods. This substantiates its potential to offer crucial insights for financial market risk management and investor guidance, consequently contributing to the mitigation of investment risks.