  We study anisotropic lattice strips in the presence of a magnetic field in
the quantum Hall effect regime. At specific magnetic fields, causing resonant
Umklapp scattering, the system is gapped in the bulk and supports chiral edge
states in close analogy to topological insulators. These gaps result in
plateaus for the Hall conductivity exactly at the known fillings n/m (both
positive integers and m odd) for the integer and fractional quantum Hall
effect. For double strips we find topological phase transitions with phases
that support midgap edge states with flat dispersion. The topological effects
predicted here could be tested directly in optical lattices.
