Objective - This study presents a biometric identification method based on topological invariants from 2D iris images, representing iris texture via formally defined digital homology and evaluating classification performance. Methods - Each normalized iris image (48x482 pixels) is divided into grids (e.g., 6x54 or 3x27). For each subregion, we compute Betti0, Betti1, and their ratio using a recent algorithm for homology groups in 2D digital images. The resulting invariants form a feature matrix used with logistic regression, KNN, and SVM (with PCA and 100 randomized repetitions). A convolutional neural network (CNN) is trained on raw images for comparison. Results - Logistic regression achieved 97.78 +/- 0.82% accuracy, outperforming CNN (96.44 +/- 1.32%) and other feature-based models. The topological features showed high accuracy with low variance. Conclusion - This is the first use of topological invariants from formal digital homology for iris recognition. The method offers a compact, interpretable, and accurate alternative to deep learning, useful when explainability or limited data is important. Beyond iris recognition, it can apply to other biometrics, medical imaging, materials science, remote sensing, and interpretable AI. It runs efficiently on CPU-only systems and produces robust, explainable features valuable for security-critical domains.