  Let G be a real form of a complex reductive group. Suppose that we are given
involutions \sigma and \theta of G. Let H=G^\sigma denote the fixed group of
\sigma and let K=G^\theta denote the fixed group of \theta. We are interested
in calculating the double coset space H\backslash G/K. We use moment map and
invariant theoretic techniques to calculate the double cosets, especially the
ones that are closed. One salient point of our results is a stratification of a
quotient of a compact torus over which the closed double cosets fiber as a
collection of trivial bundles.
