Abstract: The goal of this talk is to introduce an interesting subgroup of Aut(F_n) --- the pure symmetric automorphisms --- and outline a proof that it's a duality group. Roughly speaking, duality groups are groups whose cohomology behaves like the cohomology of a compact manifold. Given an improper group action (one where the cell stabilizers are infinite), Ken Brown and I have a criterion that implies the group is a duality group. A refinement of this idea is used to establish duality for the pure symmetric automorphism group. (Joint with Noel Brady, Jon McCammond, and Andy Miller)