3:30 p.m., Monday (27 Nov)
Exotic smooth structures on simply connected 4-dimensional manifolds
Two manifolds M and N are called homeomorphic if there
exists a bijective map f: M -> N such that both f and f^-1 are
continuous. If both f and f^-1 are smooth, then M and N are called
diffeomorphic. Note that if M and N are diffeomorphic, then they
are also homeomorphic. The converse is false. There are many
examples of a pair (M,N) such that M and N are homeomorphic but not
diffeomorphic. In this talk we will focus on dimension 4.
In particular, given a compact, simply-connected, 4-dimensional
smooth manifold (without boundary) X, we can ask whether the
underlying topological manifold X has more than one smooth structure.
By analyzing the properties of the solution spaces of certain
first-order PDE (Seiberg-Witten equations), we can show that many
such X possess infinitely many distinct smooth structures.