Michael Anderson
SUNY at Stony Brook
Dehn surgery and Einstein metrics in higher dimensions.
Abstract: Thurston's Dehn surgery theorem allows one to constuct an infinite family of compact hyperbolic 3-manifolds "near" a given complete hyperbolic 3-manifold with cusps. This is the cusp closing theorem, and nearness is measured in the (pointed) Gromov-Hausdorff topology for instance. We will show how this result can be generalized to any dimension to produce a large new class of Einstein metrics of negative scalar curvature on compact manifolds, close to any given complete hyperbolic n-manifold with cusps. (Joint work with Gordon Craig).