Topological invariants of adiabatic cycles of Bloch Hamiltonians

Invariants are constructed for various adiabatic cycles of Bloch Hamiltonians and discuss their physical implications. Many of these cycles lead to a pumping of fermions, but in other cases, the physical implications are more subtle. I also discuss the construction of these invariants for insulators in the various symmetry classes and periodicities in the table of these invariants.