Starting from the homotopical classification of defects due to M. Kléman and G. Toulouse [J. Physique 38, 195 (1977)] the author develops a global classification scheme for defects in \(n\)-dimensional ordered media by defining a “defect cocycle” and demonstrating that its cohomology class is independent of Whitehead movements [J. H. C. Whitehead, Ann. Math. (2) 41, 809–824 (1940; Zbl 0025.09203)] of the defects and that it constitutes an obstruction to their erasure by local as well as by global processes. In an appendix the classification of defects of real physical systems by homotopy groups is reviewed.