  The electronic band structure of Bi is calculated using state of the art
electronic structure methods, including density functional theory and
G$_0$W$_0$ quasiparticle approximations. The delicate ordering of states at the
L point of the Brillouin zone, which determines the topological character of
the electronic bands, is investigated in detail. The effect on the bands of
strain, changing the structural parameters of the rhombohedral crystal
structure, is shown to be important in determining this ordering and the
resulting topological character.
