## 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.