  We compute the homotopy type of the moduli space of flat, unitary connections
over aspherical surfaces, after stabilizing with respect to the rank of the
underlying bundle. Over the orientable surface M^g, we show that this space has
the homotopy type of the infinite symmetric product of M^g, generalizing a
well-known fact for the torus. Over a non-orientable surface, we show that this
space is homotopy equivalent to a disjoint union of two tori, whose common
dimension corresponds to the rank of the first (co)homology group of the
surface. Similar calculations are provided for products of surfaces, and show a
close analogy with the Quillen-Lichtenbaum conjectures in algebraic K-theory.
The proofs utilize Tyler Lawson's work in deformation K-theory, and rely
heavily on Yang-Mills theory and gauge theory.
