  Some part of the local gauge symmetries in the low energy region, say, lower
than GUT or the Planck energy can be an induced symmetry describable with the
holonomy fields associated with a topologically non-trivial structure of
partially compactified space. In the case where a six dimensional space is
compactified by the Kaluza-Klein mechanism into a product of the four
dimensional Minkowski space $M_{4}$ and a two dimensional Riemann surface with
the genus $g$, $\Sigma_{g}$, we show that, in a limit where the
compactification mass scale is sent to infinity, a model lagrangian with a U(1)
gauge symmetry produces the dynamical gauge fields in $M_{4}$ with a product of
$g$ U(1)'s symmetry, i.e., U(1)$\times \cdots\times$U(1). These fields are
induced by a Berry phase mechanism, not by the Kaluza-Klein. The dynamical
degrees of freedom of the induced fields are shown to come from the holonomies,
or the solenoid potentials, associated with the cycles of $\Sigma_{g}$. The
production mechanism of kinetic energy terms for the induced fields are
discussed in detail.
