Curvature and smooth topology in dimension four
I will discuss several differential-topological invariants of smooth compact
manifolds which arise directly out of Riemannian variational problems.
In dimension 4, these turn out to capture many of the most significant
aspects of 4-dimensional smooth topology; in particular, they often can
be used to distinguish between different smooth structures on a given topological
4-manifold. One of the recent results I will announce is a formula for
the Yamabe invariant of suitable connected sums of compact complex surfaces.
I will also describe some recent applications of these ideas to the theory
of Einstein manifolds.
Fall
2001 meeting of the PNGS