Pure Maths Colloquium: Some examples of aspherical homology 4-spheres
9 March 2009 16:15 in CM107
In this talk the construction of infinitely many examples of aspherical Riemannian 4-manifolds that are homology 4-spheres will be described. These manifolds are constructed by performing Dehn surgery on a complete, open, hyperbolic 4-manifold of finite volume which can be realized as the complement of five disjoint tori in the 4-sphere. Infinitely many of these homology 4-spheres admit an Einstein metric of negative scalar curvature. The existence of aspherical homology 4-spheres answers an old question of William Thurston and solves Problem 4.17 on Kirby's 1977 low-dimensional topology problem list. This work is joint with Steven Tschantz of Vanderbilt University.