David Gay:
Maps from 4-manifolds to the 2-sphere
There has been a recent flurry of activity surrounding various kinds
of smooth maps from 4-manifolds to the 2-sphere, starting with
Lefschetz fibrations and ending up with the rather obvious idea of
simply studying generic smooth maps to S^2 (as a generalization of
Morse theory). The idea that we should be able to get some interesting
information about 4-manifolds this way may seem naive, but I hope it
is not and I will try to present some evidence that it is not. At the
very least there are some interesting pictures to think about. The
part of the work that is original is joint with Rob Kirby, and
otherwise this will be an exposition of work by Perutz, Lekili, Baykur
and Williams, among others.