Abstract:
We will survey some joint work in progress with Stephan Stolz. For a
smooth manifold M, we define the space of all super symmetric d-dimensional
Euclidean field theories over M. We show that after dividing out a concordance
relation, the case d=0 gives de Rham cohomology and d=1 gives K-theory of M.
Finally, we explain why the case d=2 might be related to the
Hopkins-Miller-Lurie theory of topological modular forms.