  Let M be a one-holed torus with boundary $\partial M$ (a circle) and $\Gamma$
the mapping class group of M fixing $\partial M$. The group $\Gamma$ acts on
${\mathcal M}_{\mathcal C}(SU(2))$ which is the space of SU(2)-gauge
equivalence classes of flat SU(2)-connections on M with fixed holonomy on
$\partial M$. We study the topological dynamics of the $\Gamma$-action and give
conditions for the individual $\Gamma$-orbits to be dense in ${\mathcal
M}_{\mathcal C}(SU(2))$.
