We investigate the question of whether a generic countable torsion-free group admits sufficiently rich actions on topological spaces. We are motivated primarily by the problem of deciding whether or not there exists a countable torsion-free group which admits no non-trivial action on a compact manifold. We use model theoretic forcing to prove that a generic countable torsion-free group does not admit any non-trivial locally moving action on a Hausdorff topological space, and yet admits a rich Rubin poset. This is joint work with Thomas Koberda.