  When a circular ring suffers a special topological transformation, it becomes
a two-layer ring. Due to the special topology of the two-layer ring, orbital
angular momenta are allowed to be a half-integer, this would affect the
traditional Aharonov-Bohm oscillation (ABO). In this paper the fractional ABO
of the ground state energy, persistent current, and dipole transition of a
two-layer ring with two electrons has been studied. Collective and internal
coordinates $\theta_{C}$ and $\phi $ have been introduced. Based on them a very
simple formula for the current has been obtained, the symmetry constraint
imposed on the dipole transition has been clarified, a strict relation between
the photon energies of the dipole radiation and the persistent current of the
ground state has been found. Comparing with the one-layer rings, the period of
the fractional ABO of the two-layer rings becomes much shorter.
