  We present a simple exactly solvable quantum mechanical example of the global
anomaly in an $O(3)$ model with an odd number of fermionic triplets coupled to
a gauge field on a circle. Because the fundamental group is non-trivial, $\pi_1
(O(3)) ={\bf Z}_2$, fermionic level crossing or circling occur in the
eigenvalue spectrum of the 1-dim. Dirac \op under continuous external field
transformations. They are shown to be related to the presence of an odd number
of normalizable zero modes in the spectrum of an appropriate 2-dim. Dirac \op .
We argue that fermionic degrees of freedom in the presence of an infinitely
large external field violate perturbative decoupling.
