Title: Topological gravity in dimensions two and four
Author: Jack Morava
Department of Mathematics
The Johns Hopkins University
Baltimore 21218 Maryland USA
jack@math.jhu.edu
AMS classification numbers: 55P, 58D, 83C
Abstract: This is a writeup of a talk at the Utrecht
conference on Operads in June 1999: the main observation
is that the category with d-manifolds as objects, and
(d+1)-dimensional cobordisms as morphisms, is naturally
a two-category, with diffeomorphisms as the two-morphisms.
The corresponding topological category obtained by replacing
the morphism categories with their classifying spaces has
deep connections with Riemannian geometry; its monoidal
representations are the physicists' theories of topological
gravity. Five examples are sketched, four corresponding to
d=1 and one to d=3, and the paper concludes with a remark
about adjoint structures on such categories. A mistake in
some earlier papers on 2D gravity [posted in this Archive]
is noted.