  We report on the condensation of bosons in the 4th band of an optical
chequerboard lattice providing a topologically induced avoided band crossing
involving the 2nd, 3rd, and 4th Bloch bands. When the condensate is slowly
tuned through the avoided crossing, accelerated band relaxation arises and the
zero momentum approximately $C4$-invariant condensate wave function acquires
finite momentum order and reduced $C2$ symmetry. For faster tuning Landau-Zener
oscillations between different superfluid orders arise, which are used to
characterize the avoided crossing.
