CONFIGURATION SPACES OF POINTS ON THE CIRCLE AND HYPERBOLIC DEHN FILLINGS

A purely combinatorial compactification of the configuration space of n (⩾5) distinct points with equal weights in the real projective line was introduced by M. Yoshida. We geometrize it so that it will be a real hyperbolic cone-manifold of finite volume with dimension n−3. Then, we vary weights for points. The geometrization still makes sense and yields a deformation. The effectivity of deformations arisen in this manner will be locally described in the existing deformation theory of hyperbolic structures when n−3=2, 3.