Geometry, Topology and Dynamics Seminar
Igor Belegradek
Georgia Institute of Technology
Moduli spaces and non-unique souls
Abstract: We use surgery and homotopy theoretic techniques to study the moduli space of complete nonnegatively curved metrics on an open manifold N. A starting point is that the diffeomorphism type of the soul, or more generally, the diffeomorphism type of the pair (N, soul) defines a locally constant function on the moduli space. We focus on the harder case when non-diffeomorphic souls have low codimension. One of the most delicate results is an example of a simply-connected manifold with homeomorphic non-diffeomorphic souls of codimension 2. Previously, examples of homeomorphic non-diffeomorphic closed simply-connected nonnegatively curved manifolds have been only known in dimension 7 thanks to work of Kreck-Stolz, while we construct such examples in each dimension 4r-1 > 10, and realize them as codimension two souls. This is joint work with Slawomir Kwasik and Reinhard Schultz.
Wednesday November 11, 2009 at 3:00 PM in SEO 612