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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Pure Maths Colloquium: Some examples of aspherical homology 4-spheres

Presented by John Ratcliffe, Vanderbilt University (USA)

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.

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