Given a free group F and a compact Lie group K we have shown that Hom(F,K)/K
is homotopy equivalent to Hom(F,G)//G, where G is the complexification of K. In
this paper we first generalize this result to the moduli spaces of G-valued and
K-valued quiver representations. We then establish a general criterion for the
moduli of quiver representations with relations to admit such a deformation
retraction by pinching vertices.