On 2-dimensional topological field theories

Original · EN

In this paper we give a characterization of 2-dimensional topological field theories over a space X as Frobenius bundles with connections over LX, the free loop space of X. This is a generalization of the folk theorem stating that 2-dimensional topological field theories (over a point) are described by finite-dimensional commutative Frobenius algebras. In another direction, this result extends the description of 1-dimensional topological field theories over a space X as vector bundles with connections over X, cf. DST.