KTH/SU Mathematics Colloquium
06-03-29
Mattias Dahl, KTH
Surgery and Geometry
The procedure of surgery is one of the most powerful tools in the
study of smooth manifolds, leading to results such as the solution to
the Poincare conjecture in $dim \geq 5$ and the classification of
compact manifolds of a given homotopy type.
Rather surprisingly surgery can in certain cases be used to study
manifolds with additional geometric structure. The main example of
this is the case of manifolds with Riemannian metrics of positive
scalar curvature. I will discuss this and some other cases where
surgery can be applied to geometric and analytic problems.