A rapid and accurate detection of ventricular arrhythmias is essential to take appropriate therapeutic actions when cardiac arrhythmias occur. Furthermore, the accurate discrimination between arrhythmias is also important, provided that the required shocking therapy would not be the same. In this work, the main novelty is the use of the mathematical method known as Topological Data Analysis (TDA) to generate new types of features which can contribute to the improvement of the detection and classification performance of cardiac arrhythmias such as Ventricular Fibrillation (VF) and Ventricular Tachycardia (VT). The electrocardiographic (ECG) signals used for this evaluation were obtained from the standard MIT-BIH and AHA databases. Two input data to the classify are evaluated: TDA features, and Persistence Diagram Image (PDI). Using the reduced TDA-obtained features, a high average accuracy near 99% was observed when discriminating four types of rhythms (98.68% to VF; 99.05% to VT; 98.76% to normal sinus; and 99.09% to Other rhythms) with specificity values higher than 97.16% in all cases. In addition, a higher accuracy of 99.51% was obtained when discriminating between shockable (VT/VF) and non-shockable rhythms (99.03% sensitivity and 99.67% specificity). These results show that the use of TDA-derived geometric features, combined in this case this the k-Nearest Neighbor (kNN) classifier, raises the classification performance above results in previous works. Considering that these results have been achieved without preselection of ECG episodes, it can be concluded that these features may be successfully introduced in Automated External Defibrillation (AED) and Implantable Cardioverter Defibrillation (ICD) therapies