Configuration spaces of points on the circle and hyperbolic Dehn fillings, II

In our previous paper (Topology 38 (1999), 497-516), we discussed the hyperbolization of the configuration space of n (≥ 5) marked points with weights in the projective line up to projective transformations. Avariation of the weights induces a deformation. It was shown that this correspondence of the set of the weights to the Teichmüller space when n = 5 and to the Dehn filling space when n = 6 is locally one-to-one near the equal weight. In this paper, we establish its global injectivity.