  These notes accompany a lecture about the topology of symplectic (and other)
quotients. The aim is two-fold: first to advertise the ease of computation in
the symplectic category; and second to give an account of some new computations
for weighted projective spaces. We start with a brief exposition of how
orbifolds arise in the symplectic category, and discuss the techniques used to
understand their topology. We then show how these results can be used to
compute the Chen-Ruan orbifold cohomology ring of abelian symplectic
reductions. We conclude by comparing the several rings associated to a weighted
projective space. We make these computations directly, avoiding any mention of
a stacky fan or of a labeled moment polytope.
