  The two-category with three-manifolds as objects, h-cobordisms as morphisms,
and diffeomorphisms of these as two-morphisms, is extremely rich; from the
point of view of classical physics it defines a nontrivial topological model
for general relativity.
  A rather striking amount of work on pseudoisotopy theory [Hatcher,
Waldhausen, Cohen-Carlsson-Goodwillie-Hsiang-Madsen...] can be formulated as a
(generalized) TQFT in this framework. The resulting theory is far from trivial
even in the case of Minkowski space, when the relevant three-manifold is the
standard sphere.
