Connectivity of energy bands in crystals

It is shown that in crystals with nonsymmorphic space groups all energy bands corresponding to elementary band representations are composite and connected; i.e., these bands have several branches, and there are enough contact points among them so that one can travel continuously through all of them. The concept of elementary band representations is explained. The proof is essentially based on the property of monodromy occurring for families of representations of nonsymmorphic space groups.