  We show that the connection responsible for any abelian or non abelian
Aharonov-Bohm effect with $n$ parallel ``magnetic'' flux lines in $\R^3$, lies
in a trivial $G$-principal bundle $P\to M$, i.e. $P$ is isomorphic to the
product $M\times G$, where $G$ is any path connected topological group; in
particular a connected Lie group. We also show that two other bundles are
involved: the universal covering space $\tilde{M}\to M$, where path integrals
are computed, and the associated bundle $P\times_G \C^m \to M$, where the wave
function and its covariant derivative are sections.
