Introduction to topological rigidity
Mostow proved that n-dimensional closed (compact with empty boundary) Riemannian manifolds M and N with constant -1 sectional curvatures and isomorphic fundamental groups are isometric when n>2. In the more general setting where the sectional curvatures are negative but not necessarily constant, isometry is clearly too much to expect. But diffeomorphism or at least homeomorphism seemed plausible. I will discuss why homeomorphism is true when n>4. This is joint work with Lowell Jones.
Comment:This is the first of a two part lecture series. The second one will be held at IMSc on Monday, 23rd April.