Bloch theory describes the electronic states in crystals whose energies are
distributed as bands over the Brillouin zone. The electronic states
corresponding to a (few) isolated energy band(s) thus constitute a vector
bundle. The topological properties of these vector bundles provide new
characteristics of the corresponding electronic phases. We review some of these
properties in the case of (topological) insulators and semi-metals.Comment: Talk at Seminaire Poincare (Bourbaphy), Paris, June 2014,
www.bourbaphy.f
