## Topology and Geometry Seminar

Title: Flexibility and Rigidity in Gromov-Hausdorff space

Speaker: Steve Ferry

Abstract: A topological space has contractibility function \rho defined on [0, R) if every ball of radius t contracts to a point in the concentric ball of radius \rho(t). Given a dimension q, there is an epsilon so that two q-dimensional spaces with contractibility function \rho are homotopy equivalent via "small" homotopies. We give examples where such homotopy equivalent manifolds are not homeomorphic for any epsilon and show that such examples do not occur among high-dimensional manifolds with odd-torsion-free homology.