Complex Hyperbolic Cone Structures on the Configuration Spaces

The space of marked n distinct points on the complex projective line up to projective transformations will be called a configuration space. There are two families of complex hyperbolic structures on the configuration space constructed by Deligne- Mostow and by Thurston. We review that these families are the same, and then exhibit the families for n = 4, 5 in constrast with the deformation theory of real hyperbolic cone 3-manifolds

Configuration spaces of points on the circle and hyperbolic Dehn fillings

A purely combinatorial compactification of the configuration space of n (>4) 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.Comment: 22 pages, to appear in Topolog

Physics Department News, December 2006

Contents from Volume 5, Issue 2: Editor’s Note From the Chair What’s New at the University Faculty Highlights Staff Highlights PhysTEC International Week ICPEAC Program Meeting Student News Annual Student Awards Recent Graduates Department Roster Photo Gallery Feedback/Update Reply For