|Topological rigidity and its relation to geometry|
|Instructor：||Thomas Farrell [Tsinghua University]|
|Place：||Conference Room 3, floor 2|
The class on Nov 25 and 30 will be canceled.
Topological rigidity refers to situations where simple homotopy theoretic conditions determine the homeomorphism type of a manifold. The most famous being that a closed manifold homotopically equivalent to the n-dimensional sphere is homeomorphic to it. We will discuss other instances of this phenomenon and relate these to problems in Riemannian geometry.
Algebraic topology through Poincare duality and differential topology through the Whitney embedding theorem and Sard's Theorem. Some knowledge of characteristics classes (as in the text of Milnor and Stasheff) will be very useful and will be reviewed as needed.
1. Characteristic Classes by J.W. Milnor and J.D. Stasheff
2. Surgery on simply-connected manifold by W. Browder
3. Surgery on Compact Manifolds by C.T.C. Wall