Abstract The observed strong dark-to-luminous matter coupling is described by a bias relation between visible and dark matter sources. We discuss the bias which emerges in the case where the topological structure of the Universe at very large distances does not properly match that of the Friedman space. With the use of such ‘topological’ bias, we construct the universal rotation curve (URC) for spirals which happens to be in striking agreement with the empirically known URC. We also show that the topological bias explains the origin of the Tully–Fisher relation (L∼V4) and predicts peculiar oscillations in the URC with a characteristic length .