  This paper studies the canonical Chow quotient of a smooth projective variety
by a reductive algebraic group. The main purpose is to give some topological
interpretations and characterization of Chow quotient which have the advantage
to be more intuitive and geometric. This is to be done over the field of
complex numbers and in the languages that are familiar to topologists and
differential geometers.
  More precisely, the main observation of this paper is that, over the field of
complex numbers, the Chow quotient admits symplectic and other topological
interpretations, namely, symplectically, the moduli spaces of stable orbits
with prescribed momentum charges; and topologically, the moduli space of stable
action-manifolds. In addition, we give a computable characterization of the
Chow cycles of the Chow quotient, using the so-called
perturbing-translating-specializing relation.
