  We study the quantum Hall plateau transition on rectangular tori. As the
aspect ratio of the torus is increased, the two-dimensional critical behavior,
characterized by a subthermodynamic number of topological states in a vanishing
energy window around a critical energy, changes drastically. In the thin-torus
limit, the entire spectrum is Anderson-localized; however, an extensive number
of states retain a Chern number $C\neq 0$. We resolve this apparent paradox by
mapping the thin-torus quantum Hall system onto a disordered Thouless pump,
where the Chern number corresponds to the winding number of an electron's path
in real space during a pump cycle. We then characterize quantitatively the
crossover between the one- and two-dimensional regimes for large but finite
aspect ratio, where the average Thouless conductance also shows anomalous
scaling.
