Topological gravity in dimensions two and four <p>

A (two-)category with manifolds as objects 
and cobordisms as maps [and diffeomorphisms as two-morphisms] 
becomes a very interesting topological category when its 
morphism categories are replaced by their classifying spaces: 
the result is a hybrid of Segal's category and Wheeler's 
superspace. The physicists' theories of topological gravity 
are just monoidal representations of such categories: 
Kontsevich-Witten theory is the `standard' example in two 
dimensions, but classical Abel-Jacobi theory also fits 
naturally in this framework. Floer-Donaldson theory yields 
a more complicated, and interesting, example.