Contents

Abstract. Crooked planes are piecewise linear surfaces that were in-troduced by Drumm in the early 1990s to construct fundamental do-mains for properly discontinuous actions of free groups on Minkowski 3-space. In a previous paper, we introduced analogues of these sur-faces, called AdS crooked planes, in the 3-dimensional anti-de Sitter space AdS3; we showed that many properly discontinuous actions of free groups on AdS3 admit fundamental domains bounded by AdS crooked planes. Here we study further the question of which proper actions on AdS3 admit crooked fundamental domains, and show that some do not, in contrast to the Minkowski setting