We explore whether specific time-varying shape characteristics of electrocardiograms can be tapped to inform computational approaches in classifying cardiac abnormalities. In particular, we train a random forest classifier on features derived from relative differences between algebraically-computable topological signatures of consecutive segments within ECGs. We convert segments of ECGs as point cloud embeddings in high-dimensional space, extract their topological summaries, and compare these via statistical descriptors and different metrics. As part of the PhysioNet/Computing in Cardiology Challenge 2021, we (Team Cordi-Ak) test this approach across full- and reduced-lead ECGs. Using the Challenge evaluation metric, our classifiers received scores of 0.17, 0.15, 0.15, 0.15, and 0.13 (ranked 53rd, 53rd, 52nd, 52nd, and 53rd out of 100 teams) for the 12-lead, 6-lead, 4-lead, 3-lead, and 2-lead versions of the hidden validation set.