Abstract: In 1983 Jeanne Duflot published some results showing that certain long exact sequences were, in fact, short exact. Her methods confined her to smooth actions. Recently, Matthias Franz, Volker Puppe and I have needed to reconsider Duflot's results, and, in the process, we arrived at new proofs that also work for continuous actions on topological manifolds. The main tool in the proof is a spectral sequence that is an equivariant version of Poincare - Alexander - Lefschetz duality. The proof also makes use of some basic properties of Cohen - Macaulay modules and a little bit of local cohomology.