The central observation is that D-branes are not classified by integral homology because Dp-branes wrapping certain cycles suffer from a Freed-Witten anomaly, which is cancelled by the insertion of D(p-2)-branes and sometimes D(p-4)-branes that end on the afflicted Dp-brane. These inserted branes may either continue to infinity, in which case the composite object has an infinite mass, or else they may end on an anti-Dp-brane, in which case the total Dp-brane charge is zero. In either case, one may wish to remove the anomalous Dp-branes from the spectrum, leaving only a subset of the original integral cohomology.