Aaron Naber : Orbifold Regularity of Collapsed Spaces and applications to Einstein Manifolds. (Oct 14, 2008 2:55 PM)

Let (M_i,g_i) be a sequence of Riemannian n-manifolds with uniformly bounded curvature such that (M_i,g_i)->(X,d), a metric space, in the Gromov Hausdorff sense. Then we show that there is a closed subset S of X with codimension at least 3 and dimension at most n-5 such that X-S is a Riemannian Orbifold. We use this and an \epsilon-regularity theorem to show that metric spaces in the closure of the moduli space of Einstein 4-manifolds are Riemannian Orbifolds away from a finite number of points. This is joint with G. Tian.

• Category: Geometry and Topology
• Duration: 01:34:57
• Date:  October 14, 2008 at 2:55 PM
• Views: 151
• Tags:   seminar, Geometry/topology Seminar