  Let X be the moduli space of SL(n,C), SU(n), GL(n,C), or U(n)-valued
representations of a rank r free group. We classify the algebraic singular
stratification of X. This comes down to showing that the singular locus
corresponds exactly to reducible representations if there exist singularities
at all. Then by relating algebraic singularities to topological singularities,
we show the moduli spaces X generally are not topological manifolds, except for
a few examples we explicitly describe.
