Abstract: Two groups are said to have a common model geometry X when both act geometrically on the same proper geodesic metric space X. A group G is action rigid if each G’ that has a common model geometry with G is also abstractly commensurable with G; this is an example of a rigidity result which may hold in a class of groups which is not quasi-isometrically rigid. This type of result was first introduced by Stark and Woodhouse for surface amalgams in “Quasi-isometric Groups with no Common Model Geometry” (2018), and in this talk we will go over Stark and Woodhouse’s later result of action rigidity for free products of hyperbolic manifold groups. This talk is based on Stark and Woodhouse’s “Action Rigidity for Free Products of Hyperbolic Manifold Groups” (2024).