  It has been shown[19] that in a loop of length u to which a single stub of
length v is attached (fig. 1 in ref. 19), the parity effect is completely
destroyed when v/u$>2$. It was also shown that such minute topological defects
(v/u$<<1$) act as singular perturbations. However ref. 19 studies the effect of
a single topological defect and says that for v/u$<<1$ parity effect is not
violated in the ring. In this paper we show that topological defects of the
type v/u$<<1$ can also violate the parity effect depending on the exact value
of v/u and the parity effect is significantly destroyed if we have many such
geometric scatterers. This paper brings out the physical reasons for the
destruction of parity effect. We show that the generic feature of topological
defects as this is that they can produce discontinuous phase change (due to
change in energy) of the electron wavefunction in the ring for special value of
v/u and then Legett's cojecture breaks down. This may have implications on the
experimental observations.
